LEMON/LEMON-main Changeset - r936:ddd3c0d3d9bf

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Changeset - r936:ddd3c0d3d9bf

« 935:6ea176

937:122629 »

r936:ddd3c0d3d9bf

Tue, 15 Mar 2011 19:32:21

[Not Reviewed]

0 comments (0 inline)

kpeter (Peter Kovacs)
kpeter@inf.elte.hu

Implement the scaling Price Refinement heuristic in CostScaling (#417) instead of Early Termination. These two heuristics are similar, but the newer one is faster and not only makes it possible to skip some epsilon phases, but it can improve the performance of the other phases, as well.

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1 file changed with 232 insertions and 27 deletions:

lemon/cost_scaling.h

232

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lemon/cost_scaling.h

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@@ -971,48 +971,247 @@
 		      // Find active nodes (i.e. nodes with positive excess)
 		      for (int u = 0; u != _res_node_num; ++u) {
 		        if (_excess[u] > 0) _active_nodes.push_back(u);
+		      }
 		      // Initialize the next arcs
 		      for (int u = 0; u != _res_node_num; ++u) {
 		        _next_out[u] = _first_out[u];
+		      }
+		    }
 		    // Early termination heuristic
 		    bool earlyTermination() {
-		      const double EARLY_TERM_FACTOR = 3.0;
+		    // Price (potential) refinement heuristic
 		    bool priceRefinement() {
 		      // Build a static residual graph
 		      _arc_vec.clear();
 		      _cost_vec.clear();
 		      for (int j = 0; j != _res_arc_num; ++j) {
 		        if (_res_cap[j] > 0) {
 		          _arc_vec.push_back(IntPair(_source[j], _target[j]));
-		          _cost_vec.push_back(_cost[j] + 1);
+		      // Stack for stroing the topological order
 		      IntVector stack(_res_node_num);
 		      int stack_top;
 		      // Perform phases
 		      while (topologicalSort(stack, stack_top)) {
 		        // Compute node ranks in the acyclic admissible network and
 		        // store the nodes in buckets
 		        for (int i = 0; i != _res_node_num; ++i) {
 		          _rank[i] = 0;
+		        }
 		        const int bucket_end = _root + 1;
 		        for (int r = 0; r != _max_rank; ++r) {
 		          _buckets[r] = bucket_end;
+		      }
-		      _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
+		        int top_rank = 0;
 		        for ( ; stack_top >= 0; --stack_top) {
 		          int u = stack[stack_top], v;
 		          int rank_u = _rank[u];
 		      // Run Bellman-Ford algorithm to check if the current flow is optimal
 		      BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map);
 		      bf.init(0);
 		      bool done = false;
 		      int K = int(EARLY_TERM_FACTOR * std::sqrt(double(_res_node_num)));
 		      for (int i = 0; i < K && !done; ++i) {
-		        done = bf.processNextWeakRound();
+		          LargeCost rc, pi_u = _pi[u];
 		          int last_out = _first_out[u+1];
 		          for (int a = _first_out[u]; a != last_out; ++a) {
 		            if (_res_cap[a] > 0) {
 		              v = _target[a];
 		              rc = _cost[a] + pi_u - _pi[v];
 		              if (rc < 0) {
 		                LargeCost nrc = static_cast<LargeCost>((-rc - 0.5) / _epsilon);
 		                if (nrc < LargeCost(_max_rank)) {
 		                  int new_rank_v = rank_u + static_cast<int>(nrc);
 		                  if (new_rank_v > _rank[v]) {
 		                    _rank[v] = new_rank_v;
+		      }
-		      return done;
+		                }
+		              }
+		            }
+		          }
 		          if (rank_u > 0) {
 		            top_rank = std::max(top_rank, rank_u);
 		            int bfirst = _buckets[rank_u];
 		            _bucket_next[u] = bfirst;
 		            _bucket_prev[bfirst] = u;
 		            _buckets[rank_u] = u;
+		          }
+		        }
 		        // Check if the current flow is epsilon-optimal
 		        if (top_rank == 0) {
 		          return true;
+		        }
 		        // Process buckets in top-down order
 		        for (int rank = top_rank; rank > 0; --rank) {
 		          while (_buckets[rank] != bucket_end) {
 		            // Remove the first node from the current bucket
 		            int u = _buckets[rank];
 		            _buckets[rank] = _bucket_next[u];
 		            // Search the outgoing arcs of u
 		            LargeCost rc, pi_u = _pi[u];
 		            int last_out = _first_out[u+1];
 		            int v, old_rank_v, new_rank_v;
 		            for (int a = _first_out[u]; a != last_out; ++a) {
 		              if (_res_cap[a] > 0) {
 		                v = _target[a];
 		                old_rank_v = _rank[v];
 		                if (old_rank_v < rank) {
 		                  // Compute the new rank of node v
 		                  rc = _cost[a] + pi_u - _pi[v];
 		                  if (rc < 0) {
 		                    new_rank_v = rank;
 		                  } else {
 		                    LargeCost nrc = rc / _epsilon;
 		                    new_rank_v = 0;
 		                    if (nrc < LargeCost(_max_rank)) {
 		                      new_rank_v = rank - 1 - static_cast<int>(nrc);
+		                    }
+		                  }
 		                  // Change the rank of node v
 		                  if (new_rank_v > old_rank_v) {
 		                    _rank[v] = new_rank_v;
 		                    // Remove v from its old bucket
 		                    if (old_rank_v > 0) {
 		                      if (_buckets[old_rank_v] == v) {
 		                        _buckets[old_rank_v] = _bucket_next[v];
 		                      } else {
 		                        int pv = _bucket_prev[v], nv = _bucket_next[v];
 		                        _bucket_next[pv] = nv;
 		                        _bucket_prev[nv] = pv;
+		                      }
+		                    }
 		                    // Insert v into its new bucket
 		                    int nv = _buckets[new_rank_v];
 		                    _bucket_next[v] = nv;
 		                    _bucket_prev[nv] = v;
 		                    _buckets[new_rank_v] = v;
+		                  }
+		                }
+		              }
+		            }
 		            // Refine potential of node u
 		            _pi[u] -= rank * _epsilon;
+		          }
+		        }
+		      }
 		      return false;
+		    }
 		    // Find and cancel cycles in the admissible network and
 		    // determine topological order using DFS
 		    bool topologicalSort(IntVector &stack, int &stack_top) {
 		      const int MAX_CYCLE_CANCEL = 1;
 		      BoolVector reached(_res_node_num, false);
 		      BoolVector processed(_res_node_num, false);
 		      IntVector pred(_res_node_num);
 		      for (int i = 0; i != _res_node_num; ++i) {
 		        _next_out[i] = _first_out[i];
+		      }
 		      stack_top = -1;
 		      int cycle_cnt = 0;
 		      for (int start = 0; start != _res_node_num; ++start) {
 		        if (reached[start]) continue;
 		        // Start DFS search from this start node
 		        pred[start] = -1;
 		        int tip = start, v;
 		        while (true) {
 		          // Check the outgoing arcs of the current tip node
 		          reached[tip] = true;
 		          LargeCost pi_tip = _pi[tip];
 		          int a, last_out = _first_out[tip+1];
 		          for (a = _next_out[tip]; a != last_out; ++a) {
 		            if (_res_cap[a] > 0) {
 		              v = _target[a];
 		              if (_cost[a] + pi_tip - _pi[v] < 0) {
 		                if (!reached[v]) {
 		                  // A new node is reached
 		                  reached[v] = true;
 		                  pred[v] = tip;
 		                  _next_out[tip] = a;
 		                  tip = v;
 		                  a = _next_out[tip];
 		                  last_out = _first_out[tip+1];
 		                  break;
+		                }
 		                else if (!processed[v]) {
 		                  // A cycle is found
 		                  ++cycle_cnt;
 		                  _next_out[tip] = a;
 		                  // Find the minimum residual capacity along the cycle
 		                  Value d, delta = _res_cap[a];
 		                  int u, delta_node = tip;
 		                  for (u = tip; u != v; ) {
 		                    u = pred[u];
 		                    d = _res_cap[_next_out[u]];
 		                    if (d <= delta) {
 		                      delta = d;
 		                      delta_node = u;
+		                    }
+		                  }
 		                  // Augment along the cycle
 		                  _res_cap[a] -= delta;
 		                  _res_cap[_reverse[a]] += delta;
 		                  for (u = tip; u != v; ) {
 		                    u = pred[u];
 		                    int ca = _next_out[u];
 		                    _res_cap[ca] -= delta;
 		                    _res_cap[_reverse[ca]] += delta;
+		                  }
 		                  // Check the maximum number of cycle canceling
 		                  if (cycle_cnt >= MAX_CYCLE_CANCEL) {
 		                    return false;
+		                  }
 		                  // Roll back search to delta_node
 		                  if (delta_node != tip) {
 		                    for (u = tip; u != delta_node; u = pred[u]) {
 		                      reached[u] = false;
+		                    }
 		                    tip = delta_node;
 		                    a = _next_out[tip] + 1;
 		                    last_out = _first_out[tip+1];
 		                    break;
+		                  }
+		                }
+		              }
+		            }
+		          }
 		          // Step back to the previous node
 		          if (a == last_out) {
 		            processed[tip] = true;
 		            stack[++stack_top] = tip;
 		            tip = pred[tip];
 		            if (tip < 0) {
 		              // Finish DFS from the current start node
 		              break;
+		            }
 		            ++_next_out[tip];
+		          }
+		        }
+		      }
 		      return (cycle_cnt == 0);
+		    }
 		    // Global potential update heuristic
 		    void globalUpdate() {
 		      const int bucket_end = _root + 1;
 		      // Initialize buckets
 		      for (int r = 0; r != _max_rank; ++r) {
 		        _buckets[r] = bucket_end;
+		      }
 		      Value total_excess = 0;
 		      int b0 = bucket_end;
@@ -1093,40 +1292,43 @@
 		      for (int u = 0; u != _res_node_num; ++u) {
 		        int k = std::min(_rank[u], r);
 		        if (k > 0) {
 		          _pi[u] -= _epsilon * k;
 		          _next_out[u] = _first_out[u];
+		        }
+		      }
+		    }
 		    /// Execute the algorithm performing augment and relabel operations
 		    void startAugment(int max_length) {
 		      // Paramters for heuristics
-		      const int EARLY_TERM_EPSILON_LIMIT = 1000;
+		      const int PRICE_REFINEMENT_LIMIT = 2;
 		      const double GLOBAL_UPDATE_FACTOR = 1.0;
 		      const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR *
 		        (_res_node_num + _sup_node_num * _sup_node_num));
 		      int next_global_update_limit = global_update_skip;
 		      // Perform cost scaling phases
 		      IntVector path;
 		      BoolVector path_arc(_res_arc_num, false);
 		      int relabel_cnt = 0;
 		      int eps_phase_cnt = 0;
 		      for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
 : _epsilon / _alpha )
+		      {
 		        // Early termination heuristic
 		        if (_epsilon <= EARLY_TERM_EPSILON_LIMIT) {
-		          if (earlyTermination()) break;
+		        ++eps_phase_cnt;
 		        // Price refinement heuristic
 		        if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) {
 		          if (priceRefinement()) continue;
+		        }
 		        // Initialize current phase
 		        initPhase();
 		        // Perform partial augment and relabel operations
 		        while (true) {
 		          // Select an active node (FIFO selection)
 		          while (_active_nodes.size() > 0 &&
 		                 _excess[_active_nodes.front()] <= 0) {
 		            _active_nodes.pop_front();
+		          }
@@ -1215,41 +1417,44 @@
 		            globalUpdate();
 		            next_global_update_limit += global_update_skip;
+		          }
+		        }
+		      }
+		    }
 		    /// Execute the algorithm performing push and relabel operations
 		    void startPush() {
 		      // Paramters for heuristics
-		      const int EARLY_TERM_EPSILON_LIMIT = 1000;
+		      const int PRICE_REFINEMENT_LIMIT = 2;
 		      const double GLOBAL_UPDATE_FACTOR = 2.0;
 		      const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR *
 		        (_res_node_num + _sup_node_num * _sup_node_num));
 		      int next_global_update_limit = global_update_skip;
 		      // Perform cost scaling phases
 		      BoolVector hyper(_res_node_num, false);
 		      LargeCostVector hyper_cost(_res_node_num);
 		      int relabel_cnt = 0;
 		      int eps_phase_cnt = 0;
 		      for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
 : _epsilon / _alpha )
+		      {
 		        // Early termination heuristic
 		        if (_epsilon <= EARLY_TERM_EPSILON_LIMIT) {
-		          if (earlyTermination()) break;
+		        ++eps_phase_cnt;
 		        // Price refinement heuristic
 		        if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) {
 		          if (priceRefinement()) continue;
+		        }
 		        // Initialize current phase
 		        initPhase();
 		        // Perform push and relabel operations
 		        while (_active_nodes.size() > 0) {
 		          LargeCost min_red_cost, rc, pi_n;
 		          Value delta;
 		          int n, t, a, last_out = _res_arc_num;
 		        next_node:

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