[2440] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2007 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_CAPACITY_SCALING_H |
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| 20 | #define LEMON_CAPACITY_SCALING_H |
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| 21 | |
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| 22 | /// \ingroup min_cost_flow |
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| 23 | /// |
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| 24 | /// \file |
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| 25 | /// \brief The capacity scaling algorithm for finding a minimum cost |
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| 26 | /// flow. |
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| 27 | |
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[2535] | 28 | #include <lemon/graph_adaptor.h> |
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| 29 | #include <lemon/bin_heap.h> |
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[2440] | 30 | #include <vector> |
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[2457] | 31 | |
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[2440] | 32 | namespace lemon { |
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| 33 | |
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| 34 | /// \addtogroup min_cost_flow |
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| 35 | /// @{ |
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| 36 | |
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| 37 | /// \brief Implementation of the capacity scaling version of the |
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[2509] | 38 | /// successive shortest path algorithm for finding a minimum cost |
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| 39 | /// flow. |
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[2440] | 40 | /// |
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[2535] | 41 | /// \ref CapacityScaling implements the capacity scaling version |
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| 42 | /// of the successive shortest path algorithm for finding a minimum |
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| 43 | /// cost flow. |
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[2440] | 44 | /// |
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| 45 | /// \param Graph The directed graph type the algorithm runs on. |
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| 46 | /// \param LowerMap The type of the lower bound map. |
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| 47 | /// \param CapacityMap The type of the capacity (upper bound) map. |
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| 48 | /// \param CostMap The type of the cost (length) map. |
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| 49 | /// \param SupplyMap The type of the supply map. |
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| 50 | /// |
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| 51 | /// \warning |
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| 52 | /// - Edge capacities and costs should be nonnegative integers. |
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[2535] | 53 | /// However \c CostMap::Value should be signed type. |
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[2509] | 54 | /// - Supply values should be signed integers. |
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[2440] | 55 | /// - \c LowerMap::Value must be convertible to |
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[2535] | 56 | /// \c CapacityMap::Value and \c CapacityMap::Value must be |
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| 57 | /// convertible to \c SupplyMap::Value. |
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[2440] | 58 | /// |
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| 59 | /// \author Peter Kovacs |
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| 60 | |
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[2533] | 61 | template < typename Graph, |
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[2535] | 62 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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| 63 | typename CapacityMap = LowerMap, |
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| 64 | typename CostMap = typename Graph::template EdgeMap<int>, |
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| 65 | typename SupplyMap = typename Graph::template NodeMap |
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| 66 | <typename CapacityMap::Value> > |
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[2440] | 67 | class CapacityScaling |
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| 68 | { |
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| 69 | typedef typename Graph::Node Node; |
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| 70 | typedef typename Graph::NodeIt NodeIt; |
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| 71 | typedef typename Graph::Edge Edge; |
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| 72 | typedef typename Graph::EdgeIt EdgeIt; |
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| 73 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 74 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 75 | |
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| 76 | typedef typename LowerMap::Value Lower; |
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| 77 | typedef typename CapacityMap::Value Capacity; |
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| 78 | typedef typename CostMap::Value Cost; |
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| 79 | typedef typename SupplyMap::Value Supply; |
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| 80 | typedef typename Graph::template EdgeMap<Capacity> CapacityRefMap; |
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| 81 | typedef typename Graph::template NodeMap<Supply> SupplyRefMap; |
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[2535] | 82 | typedef typename Graph::template NodeMap<Edge> PredMap; |
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[2440] | 83 | |
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| 84 | public: |
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| 85 | |
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[2535] | 86 | /// \brief Type to enable or disable capacity scaling. |
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| 87 | enum ScalingEnum { |
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| 88 | WITH_SCALING = 0, |
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| 89 | WITHOUT_SCALING = -1 |
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| 90 | }; |
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| 91 | |
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[2440] | 92 | /// \brief The type of the flow map. |
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| 93 | typedef CapacityRefMap FlowMap; |
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| 94 | /// \brief The type of the potential map. |
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| 95 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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| 96 | |
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| 97 | protected: |
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| 98 | |
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[2535] | 99 | /// \brief Special implementation of the \ref Dijkstra algorithm |
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| 100 | /// for finding shortest paths in the residual network of the graph |
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| 101 | /// with respect to the reduced edge costs and modifying the |
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| 102 | /// node potentials according to the distance of the nodes. |
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| 103 | class ResidualDijkstra |
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[2440] | 104 | { |
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[2535] | 105 | typedef typename Graph::template NodeMap<Cost> CostNodeMap; |
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| 106 | typedef typename Graph::template NodeMap<Edge> PredMap; |
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[2440] | 107 | |
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[2535] | 108 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
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| 109 | typedef BinHeap<Cost, HeapCrossRef> Heap; |
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| 110 | |
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| 111 | protected: |
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| 112 | |
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| 113 | /// \brief The directed graph the algorithm runs on. |
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| 114 | const Graph &graph; |
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| 115 | |
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| 116 | /// \brief The flow map. |
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| 117 | const FlowMap &flow; |
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| 118 | /// \brief The residual capacity map. |
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| 119 | const CapacityRefMap &res_cap; |
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| 120 | /// \brief The cost map. |
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| 121 | const CostMap &cost; |
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| 122 | /// \brief The excess map. |
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| 123 | const SupplyRefMap &excess; |
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| 124 | |
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| 125 | /// \brief The potential map. |
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| 126 | PotentialMap &potential; |
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| 127 | |
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| 128 | /// \brief The distance map. |
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| 129 | CostNodeMap dist; |
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| 130 | /// \brief The map of predecessors edges. |
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| 131 | PredMap &pred; |
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| 132 | /// \brief The processed (i.e. permanently labeled) nodes. |
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| 133 | std::vector<Node> proc_nodes; |
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[2440] | 134 | |
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| 135 | public: |
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| 136 | |
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[2535] | 137 | /// \brief The constructor of the class. |
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| 138 | ResidualDijkstra( const Graph &_graph, |
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| 139 | const FlowMap &_flow, |
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| 140 | const CapacityRefMap &_res_cap, |
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| 141 | const CostMap &_cost, |
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| 142 | const SupplyMap &_excess, |
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| 143 | PotentialMap &_potential, |
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| 144 | PredMap &_pred ) : |
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| 145 | graph(_graph), flow(_flow), res_cap(_res_cap), cost(_cost), |
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| 146 | excess(_excess), potential(_potential), dist(_graph), |
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| 147 | pred(_pred) |
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| 148 | {} |
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[2440] | 149 | |
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[2535] | 150 | /// \brief Runs the algorithm from the given source node. |
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| 151 | Node run(Node s, Capacity delta) { |
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| 152 | HeapCrossRef heap_cross_ref(graph, Heap::PRE_HEAP); |
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| 153 | Heap heap(heap_cross_ref); |
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| 154 | heap.push(s, 0); |
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| 155 | pred[s] = INVALID; |
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| 156 | proc_nodes.clear(); |
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| 157 | |
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| 158 | // Processing nodes |
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| 159 | while (!heap.empty() && excess[heap.top()] > -delta) { |
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| 160 | Node u = heap.top(), v; |
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| 161 | Cost d = heap.prio() - potential[u], nd; |
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| 162 | dist[u] = heap.prio(); |
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| 163 | heap.pop(); |
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| 164 | proc_nodes.push_back(u); |
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| 165 | |
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| 166 | // Traversing outgoing edges |
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| 167 | for (OutEdgeIt e(graph, u); e != INVALID; ++e) { |
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| 168 | if (res_cap[e] >= delta) { |
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| 169 | v = graph.target(e); |
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| 170 | switch(heap.state(v)) { |
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| 171 | case Heap::PRE_HEAP: |
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| 172 | heap.push(v, d + cost[e] + potential[v]); |
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| 173 | pred[v] = e; |
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| 174 | break; |
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| 175 | case Heap::IN_HEAP: |
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| 176 | nd = d + cost[e] + potential[v]; |
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| 177 | if (nd < heap[v]) { |
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| 178 | heap.decrease(v, nd); |
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| 179 | pred[v] = e; |
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| 180 | } |
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| 181 | break; |
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| 182 | case Heap::POST_HEAP: |
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| 183 | break; |
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| 184 | } |
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| 185 | } |
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| 186 | } |
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| 187 | |
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| 188 | // Traversing incoming edges |
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| 189 | for (InEdgeIt e(graph, u); e != INVALID; ++e) { |
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| 190 | if (flow[e] >= delta) { |
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| 191 | v = graph.source(e); |
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| 192 | switch(heap.state(v)) { |
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| 193 | case Heap::PRE_HEAP: |
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| 194 | heap.push(v, d - cost[e] + potential[v]); |
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| 195 | pred[v] = e; |
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| 196 | break; |
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| 197 | case Heap::IN_HEAP: |
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| 198 | nd = d - cost[e] + potential[v]; |
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| 199 | if (nd < heap[v]) { |
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| 200 | heap.decrease(v, nd); |
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| 201 | pred[v] = e; |
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| 202 | } |
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| 203 | break; |
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| 204 | case Heap::POST_HEAP: |
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| 205 | break; |
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| 206 | } |
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| 207 | } |
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| 208 | } |
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| 209 | } |
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| 210 | if (heap.empty()) return INVALID; |
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| 211 | |
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| 212 | // Updating potentials of processed nodes |
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| 213 | Node t = heap.top(); |
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| 214 | Cost dt = heap.prio(); |
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| 215 | for (int i = 0; i < proc_nodes.size(); ++i) |
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| 216 | potential[proc_nodes[i]] -= dist[proc_nodes[i]] - dt; |
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| 217 | |
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| 218 | return t; |
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[2440] | 219 | } |
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| 220 | |
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[2535] | 221 | }; //class ResidualDijkstra |
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[2440] | 222 | |
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| 223 | protected: |
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| 224 | |
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| 225 | /// \brief The directed graph the algorithm runs on. |
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| 226 | const Graph &graph; |
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| 227 | /// \brief The original lower bound map. |
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| 228 | const LowerMap *lower; |
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| 229 | /// \brief The modified capacity map. |
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| 230 | CapacityRefMap capacity; |
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| 231 | /// \brief The cost map. |
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| 232 | const CostMap &cost; |
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| 233 | /// \brief The modified supply map. |
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| 234 | SupplyRefMap supply; |
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| 235 | /// \brief The sum of supply values equals zero. |
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| 236 | bool valid_supply; |
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| 237 | |
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| 238 | /// \brief The edge map of the current flow. |
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| 239 | FlowMap flow; |
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| 240 | /// \brief The potential node map. |
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| 241 | PotentialMap potential; |
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| 242 | |
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[2535] | 243 | /// \brief The residual capacity map. |
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| 244 | CapacityRefMap res_cap; |
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| 245 | /// \brief The excess map. |
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| 246 | SupplyRefMap excess; |
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| 247 | /// \brief The excess nodes (i.e. nodes with positive excess). |
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| 248 | std::vector<Node> excess_nodes; |
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[2440] | 249 | /// \brief The index of the next excess node. |
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| 250 | int next_node; |
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| 251 | |
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[2535] | 252 | /// \brief The scaling status (enabled or disabled). |
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| 253 | ScalingEnum scaling; |
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[2440] | 254 | /// \brief The delta parameter used for capacity scaling. |
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| 255 | Capacity delta; |
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[2535] | 256 | /// \brief The maximum number of phases. |
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| 257 | Capacity phase_num; |
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| 258 | /// \brief The deficit nodes. |
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| 259 | std::vector<Node> deficit_nodes; |
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[2440] | 260 | |
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[2535] | 261 | /// \brief Implementation of the \ref Dijkstra algorithm for |
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| 262 | /// finding augmenting shortest paths in the residual network. |
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| 263 | ResidualDijkstra dijkstra; |
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| 264 | /// \brief The map of predecessors edges. |
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| 265 | PredMap pred; |
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[2440] | 266 | |
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| 267 | public : |
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| 268 | |
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| 269 | /// \brief General constructor of the class (with lower bounds). |
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| 270 | /// |
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| 271 | /// General constructor of the class (with lower bounds). |
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| 272 | /// |
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| 273 | /// \param _graph The directed graph the algorithm runs on. |
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| 274 | /// \param _lower The lower bounds of the edges. |
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| 275 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 276 | /// \param _cost The cost (length) values of the edges. |
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| 277 | /// \param _supply The supply values of the nodes (signed). |
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| 278 | CapacityScaling( const Graph &_graph, |
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[2535] | 279 | const LowerMap &_lower, |
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| 280 | const CapacityMap &_capacity, |
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| 281 | const CostMap &_cost, |
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| 282 | const SupplyMap &_supply ) : |
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[2440] | 283 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
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| 284 | supply(_graph), flow(_graph, 0), potential(_graph, 0), |
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[2535] | 285 | res_cap(_graph), excess(_graph), pred(_graph), |
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| 286 | dijkstra(graph, flow, res_cap, cost, excess, potential, pred) |
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[2440] | 287 | { |
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| 288 | // Removing nonzero lower bounds |
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| 289 | capacity = subMap(_capacity, _lower); |
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[2535] | 290 | res_cap = capacity; |
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[2440] | 291 | Supply sum = 0; |
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| 292 | for (NodeIt n(graph); n != INVALID; ++n) { |
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[2535] | 293 | Supply s = _supply[n]; |
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| 294 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
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| 295 | s += _lower[e]; |
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| 296 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
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| 297 | s -= _lower[e]; |
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| 298 | supply[n] = s; |
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| 299 | sum += s; |
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[2440] | 300 | } |
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| 301 | valid_supply = sum == 0; |
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| 302 | } |
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| 303 | |
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| 304 | /// \brief General constructor of the class (without lower bounds). |
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| 305 | /// |
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| 306 | /// General constructor of the class (without lower bounds). |
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| 307 | /// |
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| 308 | /// \param _graph The directed graph the algorithm runs on. |
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| 309 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 310 | /// \param _cost The cost (length) values of the edges. |
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| 311 | /// \param _supply The supply values of the nodes (signed). |
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| 312 | CapacityScaling( const Graph &_graph, |
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[2535] | 313 | const CapacityMap &_capacity, |
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| 314 | const CostMap &_cost, |
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| 315 | const SupplyMap &_supply ) : |
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[2440] | 316 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
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| 317 | supply(_supply), flow(_graph, 0), potential(_graph, 0), |
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[2535] | 318 | res_cap(_capacity), excess(_graph), pred(_graph), |
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| 319 | dijkstra(graph, flow, res_cap, cost, excess, potential) |
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[2440] | 320 | { |
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| 321 | // Checking the sum of supply values |
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| 322 | Supply sum = 0; |
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| 323 | for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n]; |
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| 324 | valid_supply = sum == 0; |
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| 325 | } |
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| 326 | |
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| 327 | /// \brief Simple constructor of the class (with lower bounds). |
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| 328 | /// |
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| 329 | /// Simple constructor of the class (with lower bounds). |
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| 330 | /// |
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| 331 | /// \param _graph The directed graph the algorithm runs on. |
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| 332 | /// \param _lower The lower bounds of the edges. |
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| 333 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 334 | /// \param _cost The cost (length) values of the edges. |
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| 335 | /// \param _s The source node. |
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| 336 | /// \param _t The target node. |
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| 337 | /// \param _flow_value The required amount of flow from node \c _s |
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| 338 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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| 339 | /// \c _t). |
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| 340 | CapacityScaling( const Graph &_graph, |
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[2535] | 341 | const LowerMap &_lower, |
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| 342 | const CapacityMap &_capacity, |
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| 343 | const CostMap &_cost, |
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| 344 | Node _s, Node _t, |
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| 345 | Supply _flow_value ) : |
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[2440] | 346 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
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| 347 | supply(_graph), flow(_graph, 0), potential(_graph, 0), |
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[2535] | 348 | res_cap(_graph), excess(_graph), pred(_graph), |
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| 349 | dijkstra(graph, flow, res_cap, cost, excess, potential) |
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[2440] | 350 | { |
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| 351 | // Removing nonzero lower bounds |
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| 352 | capacity = subMap(_capacity, _lower); |
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[2535] | 353 | res_cap = capacity; |
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[2440] | 354 | for (NodeIt n(graph); n != INVALID; ++n) { |
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[2535] | 355 | Supply s = 0; |
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| 356 | if (n == _s) s = _flow_value; |
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| 357 | if (n == _t) s = -_flow_value; |
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| 358 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
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| 359 | s += _lower[e]; |
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| 360 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
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| 361 | s -= _lower[e]; |
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| 362 | supply[n] = s; |
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[2440] | 363 | } |
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| 364 | valid_supply = true; |
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| 365 | } |
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| 366 | |
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| 367 | /// \brief Simple constructor of the class (without lower bounds). |
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| 368 | /// |
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| 369 | /// Simple constructor of the class (without lower bounds). |
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| 370 | /// |
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| 371 | /// \param _graph The directed graph the algorithm runs on. |
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| 372 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 373 | /// \param _cost The cost (length) values of the edges. |
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| 374 | /// \param _s The source node. |
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| 375 | /// \param _t The target node. |
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| 376 | /// \param _flow_value The required amount of flow from node \c _s |
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| 377 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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| 378 | /// \c _t). |
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| 379 | CapacityScaling( const Graph &_graph, |
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[2535] | 380 | const CapacityMap &_capacity, |
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| 381 | const CostMap &_cost, |
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| 382 | Node _s, Node _t, |
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| 383 | Supply _flow_value ) : |
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[2440] | 384 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
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| 385 | supply(_graph, 0), flow(_graph, 0), potential(_graph, 0), |
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[2535] | 386 | res_cap(_capacity), excess(_graph), pred(_graph), |
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| 387 | dijkstra(graph, flow, res_cap, cost, excess, potential) |
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[2440] | 388 | { |
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| 389 | supply[_s] = _flow_value; |
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| 390 | supply[_t] = -_flow_value; |
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| 391 | valid_supply = true; |
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| 392 | } |
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| 393 | |
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| 394 | /// \brief Returns a const reference to the flow map. |
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| 395 | /// |
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| 396 | /// Returns a const reference to the flow map. |
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| 397 | /// |
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| 398 | /// \pre \ref run() must be called before using this function. |
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| 399 | const FlowMap& flowMap() const { |
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| 400 | return flow; |
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| 401 | } |
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| 402 | |
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| 403 | /// \brief Returns a const reference to the potential map (the dual |
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| 404 | /// solution). |
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| 405 | /// |
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| 406 | /// Returns a const reference to the potential map (the dual |
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| 407 | /// solution). |
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| 408 | /// |
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| 409 | /// \pre \ref run() must be called before using this function. |
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| 410 | const PotentialMap& potentialMap() const { |
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| 411 | return potential; |
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| 412 | } |
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| 413 | |
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| 414 | /// \brief Returns the total cost of the found flow. |
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| 415 | /// |
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| 416 | /// Returns the total cost of the found flow. The complexity of the |
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| 417 | /// function is \f$ O(e) \f$. |
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| 418 | /// |
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| 419 | /// \pre \ref run() must be called before using this function. |
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| 420 | Cost totalCost() const { |
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| 421 | Cost c = 0; |
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| 422 | for (EdgeIt e(graph); e != INVALID; ++e) |
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[2535] | 423 | c += flow[e] * cost[e]; |
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[2440] | 424 | return c; |
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| 425 | } |
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| 426 | |
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[2457] | 427 | /// \brief Runs the algorithm. |
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[2440] | 428 | /// |
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[2457] | 429 | /// Runs the algorithm. |
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[2440] | 430 | /// |
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[2535] | 431 | /// \param scaling_mode The scaling mode. In case of WITH_SCALING |
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| 432 | /// capacity scaling is enabled in the algorithm (this is the |
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| 433 | /// default value) otherwise it is disabled. |
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| 434 | /// If the maximum edge capacity and/or the amount of total supply |
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| 435 | /// is small, the algorithm could be faster without scaling. |
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| 436 | /// |
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[2440] | 437 | /// \return \c true if a feasible flow can be found. |
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[2535] | 438 | bool run(int scaling_mode = WITH_SCALING) { |
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| 439 | return init(scaling_mode) && start(); |
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[2440] | 440 | } |
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| 441 | |
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| 442 | protected: |
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| 443 | |
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| 444 | /// \brief Initializes the algorithm. |
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[2535] | 445 | bool init(int scaling_mode) { |
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[2440] | 446 | if (!valid_supply) return false; |
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[2535] | 447 | excess = supply; |
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[2440] | 448 | |
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| 449 | // Initilaizing delta value |
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[2535] | 450 | if (scaling_mode == WITH_SCALING) { |
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| 451 | // With scaling |
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| 452 | Supply max_sup = 0, max_dem = 0; |
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| 453 | for (NodeIt n(graph); n != INVALID; ++n) { |
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| 454 | if ( supply[n] > max_sup) max_sup = supply[n]; |
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| 455 | if (-supply[n] > max_dem) max_dem = -supply[n]; |
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| 456 | } |
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| 457 | if (max_dem < max_sup) max_sup = max_dem; |
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| 458 | phase_num = 0; |
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| 459 | for (delta = 1; 2 * delta <= max_sup; delta *= 2) |
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| 460 | ++phase_num; |
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| 461 | } else { |
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| 462 | // Without scaling |
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| 463 | delta = 1; |
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[2440] | 464 | } |
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| 465 | return true; |
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| 466 | } |
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| 467 | |
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[2535] | 468 | /// \brief Executes the algorithm. |
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| 469 | bool start() { |
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| 470 | if (delta > 1) |
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| 471 | return startWithScaling(); |
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| 472 | else |
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| 473 | return startWithoutScaling(); |
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| 474 | } |
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| 475 | |
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| 476 | /// \brief Executes the capacity scaling version of the successive |
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| 477 | /// shortest path algorithm. |
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| 478 | bool startWithScaling() { |
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| 479 | // Processing capacity scaling phases |
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| 480 | Node s, t; |
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| 481 | int phase_cnt = 0; |
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| 482 | int factor = 4; |
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| 483 | while (true) { |
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| 484 | // Saturating all edges not satisfying the optimality condition |
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| 485 | for (EdgeIt e(graph); e != INVALID; ++e) { |
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| 486 | Node u = graph.source(e), v = graph.target(e); |
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| 487 | Cost c = cost[e] - potential[u] + potential[v]; |
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| 488 | if (c < 0 && res_cap[e] >= delta) { |
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| 489 | excess[u] -= res_cap[e]; |
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| 490 | excess[v] += res_cap[e]; |
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| 491 | flow[e] = capacity[e]; |
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| 492 | res_cap[e] = 0; |
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| 493 | } |
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| 494 | else if (c > 0 && flow[e] >= delta) { |
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| 495 | excess[u] += flow[e]; |
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| 496 | excess[v] -= flow[e]; |
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| 497 | flow[e] = 0; |
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| 498 | res_cap[e] = capacity[e]; |
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| 499 | } |
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| 500 | } |
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| 501 | |
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| 502 | // Finding excess nodes and deficit nodes |
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| 503 | excess_nodes.clear(); |
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| 504 | deficit_nodes.clear(); |
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| 505 | for (NodeIt n(graph); n != INVALID; ++n) { |
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| 506 | if (excess[n] >= delta) excess_nodes.push_back(n); |
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| 507 | if (excess[n] <= -delta) deficit_nodes.push_back(n); |
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| 508 | } |
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| 509 | next_node = 0; |
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| 510 | |
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| 511 | // Finding augmenting shortest paths |
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| 512 | while (next_node < excess_nodes.size()) { |
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| 513 | // Checking deficit nodes |
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| 514 | if (delta > 1) { |
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| 515 | bool delta_deficit = false; |
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| 516 | for (int i = 0; i < deficit_nodes.size(); ++i) { |
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| 517 | if (excess[deficit_nodes[i]] <= -delta) { |
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| 518 | delta_deficit = true; |
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| 519 | break; |
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| 520 | } |
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| 521 | } |
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| 522 | if (!delta_deficit) break; |
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| 523 | } |
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| 524 | |
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| 525 | // Running Dijkstra |
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| 526 | s = excess_nodes[next_node]; |
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| 527 | if ((t = dijkstra.run(s, delta)) == INVALID) { |
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| 528 | if (delta > 1) { |
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| 529 | ++next_node; |
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| 530 | continue; |
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| 531 | } |
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| 532 | return false; |
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| 533 | } |
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| 534 | |
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| 535 | // Augmenting along a shortest path from s to t. |
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| 536 | Capacity d = excess[s] < -excess[t] ? excess[s] : -excess[t]; |
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| 537 | Node u = t; |
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| 538 | Edge e; |
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| 539 | if (d > delta) { |
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| 540 | while ((e = pred[u]) != INVALID) { |
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| 541 | Capacity rc; |
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| 542 | if (u == graph.target(e)) { |
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| 543 | rc = res_cap[e]; |
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| 544 | u = graph.source(e); |
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| 545 | } else { |
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| 546 | rc = flow[e]; |
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| 547 | u = graph.target(e); |
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| 548 | } |
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| 549 | if (rc < d) d = rc; |
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| 550 | } |
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| 551 | } |
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| 552 | u = t; |
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| 553 | while ((e = pred[u]) != INVALID) { |
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| 554 | if (u == graph.target(e)) { |
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| 555 | flow[e] += d; |
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| 556 | res_cap[e] -= d; |
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| 557 | u = graph.source(e); |
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| 558 | } else { |
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| 559 | flow[e] -= d; |
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| 560 | res_cap[e] += d; |
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| 561 | u = graph.target(e); |
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| 562 | } |
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| 563 | } |
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| 564 | excess[s] -= d; |
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| 565 | excess[t] += d; |
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| 566 | |
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| 567 | if (excess[s] < delta) ++next_node; |
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| 568 | } |
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| 569 | |
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| 570 | if (delta == 1) break; |
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| 571 | if (++phase_cnt > phase_num / 4) factor = 2; |
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| 572 | delta = delta <= factor ? 1 : delta / factor; |
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| 573 | } |
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| 574 | |
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| 575 | // Handling nonzero lower bounds |
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| 576 | if (lower) { |
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| 577 | for (EdgeIt e(graph); e != INVALID; ++e) |
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| 578 | flow[e] += (*lower)[e]; |
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| 579 | } |
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| 580 | return true; |
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| 581 | } |
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| 582 | |
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[2440] | 583 | /// \brief Executes the successive shortest path algorithm without |
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| 584 | /// capacity scaling. |
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[2535] | 585 | bool startWithoutScaling() { |
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[2440] | 586 | // Finding excess nodes |
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[2535] | 587 | for (NodeIt n(graph); n != INVALID; ++n) { |
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| 588 | if (excess[n] > 0) excess_nodes.push_back(n); |
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[2440] | 589 | } |
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| 590 | if (excess_nodes.size() == 0) return true; |
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| 591 | next_node = 0; |
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| 592 | |
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[2457] | 593 | // Finding shortest paths |
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[2535] | 594 | Node s, t; |
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| 595 | while ( excess[excess_nodes[next_node]] > 0 || |
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| 596 | ++next_node < excess_nodes.size() ) |
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[2440] | 597 | { |
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[2535] | 598 | // Running Dijkstra |
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| 599 | s = excess_nodes[next_node]; |
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| 600 | if ((t = dijkstra.run(s, 1)) == INVALID) |
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| 601 | return false; |
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[2440] | 602 | |
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[2535] | 603 | // Augmenting along a shortest path from s to t |
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| 604 | Capacity d = excess[s] < -excess[t] ? excess[s] : -excess[t]; |
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| 605 | Node u = t; |
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| 606 | Edge e; |
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| 607 | while ((e = pred[u]) != INVALID) { |
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| 608 | Capacity rc; |
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| 609 | if (u == graph.target(e)) { |
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| 610 | rc = res_cap[e]; |
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| 611 | u = graph.source(e); |
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| 612 | } else { |
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| 613 | rc = flow[e]; |
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| 614 | u = graph.target(e); |
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| 615 | } |
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| 616 | if (rc < d) d = rc; |
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| 617 | } |
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| 618 | u = t; |
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| 619 | while ((e = pred[u]) != INVALID) { |
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| 620 | if (u == graph.target(e)) { |
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| 621 | flow[e] += d; |
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| 622 | res_cap[e] -= d; |
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| 623 | u = graph.source(e); |
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| 624 | } else { |
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| 625 | flow[e] -= d; |
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| 626 | res_cap[e] += d; |
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| 627 | u = graph.target(e); |
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| 628 | } |
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| 629 | } |
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| 630 | excess[s] -= d; |
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| 631 | excess[t] += d; |
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[2440] | 632 | } |
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| 633 | |
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| 634 | // Handling nonzero lower bounds |
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| 635 | if (lower) { |
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[2535] | 636 | for (EdgeIt e(graph); e != INVALID; ++e) |
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| 637 | flow[e] += (*lower)[e]; |
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[2440] | 638 | } |
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| 639 | return true; |
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| 640 | } |
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| 641 | |
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| 642 | }; //class CapacityScaling |
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| 643 | |
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| 644 | ///@} |
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| 645 | |
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| 646 | } //namespace lemon |
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| 647 | |
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| 648 | #endif //LEMON_CAPACITY_SCALING_H |
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