test/suurballe_test.cc
author Alpar Juttner <alpar@cs.elte.hu>
Fri, 20 Feb 2009 21:37:19 +0000
changeset 517 2b6d5d22bb23
parent 423 ff48c2738fb2
child 623 7c1324b35d89
permissions -rw-r--r--
Merge
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2009
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#include <iostream>
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#include <lemon/list_graph.h>
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#include <lemon/lgf_reader.h>
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#include <lemon/path.h>
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#include <lemon/suurballe.h>
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#include "test_tools.h"
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using namespace lemon;
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char test_lgf[] =
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  "@nodes\n"
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  "label supply1 supply2 supply3\n"
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  "1     0        20      27\n"
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  "2     0       -4        0\n"
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  "3     0        0        0\n"
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  "4     0        0        0\n"
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  "5     0        9        0\n"
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  "6     0       -6        0\n"
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  "7     0        0        0\n"
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  "8     0        0        0\n"
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  "9     0        3        0\n"
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  "10    0       -2        0\n"
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  "11    0        0        0\n"
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  "12    0       -20     -27\n"
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  "@arcs\n"
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  "      cost capacity lower1 lower2\n"
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  " 1  2  70  11       0      8\n"
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  " 1  3 150   3       0      1\n"
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  " 1  4  80  15       0      2\n"
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  " 2  8  80  12       0      0\n"
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  " 3  5 140   5       0      3\n"
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  " 4  6  60  10       0      1\n"
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  " 4  7  80   2       0      0\n"
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  " 4  8 110   3       0      0\n"
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  " 5  7  60  14       0      0\n"
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  " 5 11 120  12       0      0\n"
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  " 6  3   0   3       0      0\n"
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  " 6  9 140   4       0      0\n"
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  " 6 10  90   8       0      0\n"
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  " 7  1  30   5       0      0\n"
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  " 8 12  60  16       0      4\n"
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  " 9 12  50   6       0      0\n"
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  "10 12  70  13       0      5\n"
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  "10  2 100   7       0      0\n"
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  "10  7  60  10       0      0\n"
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  "11 10  20  14       0      6\n"
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  "12 11  30  10       0      0\n"
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  "@attributes\n"
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  "source  1\n"
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  "target 12\n"
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  "@end\n";
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// Check the feasibility of the flow
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template <typename Digraph, typename FlowMap>
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bool checkFlow( const Digraph& gr, const FlowMap& flow,
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                typename Digraph::Node s, typename Digraph::Node t,
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                int value )
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{
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  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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  for (ArcIt e(gr); e != INVALID; ++e)
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    if (!(flow[e] == 0 || flow[e] == 1)) return false;
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  for (NodeIt n(gr); n != INVALID; ++n) {
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    int sum = 0;
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    for (OutArcIt e(gr, n); e != INVALID; ++e)
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      sum += flow[e];
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    for (InArcIt e(gr, n); e != INVALID; ++e)
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      sum -= flow[e];
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    if (n == s && sum != value) return false;
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    if (n == t && sum != -value) return false;
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    if (n != s && n != t && sum != 0) return false;
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  }
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  return true;
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}
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// Check the optimalitiy of the flow
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template < typename Digraph, typename CostMap,
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           typename FlowMap, typename PotentialMap >
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bool checkOptimality( const Digraph& gr, const CostMap& cost,
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                      const FlowMap& flow, const PotentialMap& pi )
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{
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  // Check the "Complementary Slackness" optimality condition
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  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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  bool opt = true;
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  for (ArcIt e(gr); e != INVALID; ++e) {
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    typename CostMap::Value red_cost =
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      cost[e] + pi[gr.source(e)] - pi[gr.target(e)];
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    opt = (flow[e] == 0 && red_cost >= 0) ||
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          (flow[e] == 1 && red_cost <= 0);
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    if (!opt) break;
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  }
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  return opt;
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}
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// Check a path
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template <typename Digraph, typename Path>
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bool checkPath( const Digraph& gr, const Path& path,
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                typename Digraph::Node s, typename Digraph::Node t)
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{
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  // Check the "Complementary Slackness" optimality condition
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  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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  Node n = s;
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  for (int i = 0; i < path.length(); ++i) {
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    if (gr.source(path.nth(i)) != n) return false;
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    n = gr.target(path.nth(i));
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  }
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  return n == t;
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}
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int main()
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{
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  DIGRAPH_TYPEDEFS(ListDigraph);
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  // Read the test digraph
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  ListDigraph digraph;
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  ListDigraph::ArcMap<int> length(digraph);
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  Node source, target;
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  std::istringstream input(test_lgf);
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  DigraphReader<ListDigraph>(digraph, input).
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    arcMap("cost", length).
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    node("source", source).
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    node("target", target).
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    run();
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  // Find 2 paths
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  {
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    Suurballe<ListDigraph> suurballe(digraph, length, source, target);
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    check(suurballe.run(2) == 2, "Wrong number of paths");
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    check(checkFlow(digraph, suurballe.flowMap(), source, target, 2),
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          "The flow is not feasible");
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    check(suurballe.totalLength() == 510, "The flow is not optimal");
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    check(checkOptimality(digraph, length, suurballe.flowMap(),
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                          suurballe.potentialMap()),
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          "Wrong potentials");
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    for (int i = 0; i < suurballe.pathNum(); ++i)
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      check(checkPath(digraph, suurballe.path(i), source, target),
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            "Wrong path");
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  }
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  // Find 3 paths
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  {
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    Suurballe<ListDigraph> suurballe(digraph, length, source, target);
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    check(suurballe.run(3) == 3, "Wrong number of paths");
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    check(checkFlow(digraph, suurballe.flowMap(), source, target, 3),
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          "The flow is not feasible");
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    check(suurballe.totalLength() == 1040, "The flow is not optimal");
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    check(checkOptimality(digraph, length, suurballe.flowMap(),
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                          suurballe.potentialMap()),
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          "Wrong potentials");
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    for (int i = 0; i < suurballe.pathNum(); ++i)
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      check(checkPath(digraph, suurballe.path(i), source, target),
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            "Wrong path");
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  }
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  // Find 5 paths (only 3 can be found)
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  {
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    Suurballe<ListDigraph> suurballe(digraph, length, source, target);
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    check(suurballe.run(5) == 3, "Wrong number of paths");
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    check(checkFlow(digraph, suurballe.flowMap(), source, target, 3),
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          "The flow is not feasible");
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    check(suurballe.totalLength() == 1040, "The flow is not optimal");
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    check(checkOptimality(digraph, length, suurballe.flowMap(),
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                          suurballe.potentialMap()),
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          "Wrong potentials");
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    for (int i = 0; i < suurballe.pathNum(); ++i)
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      check(checkPath(digraph, suurballe.path(i), source, target),
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            "Wrong path");
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  }
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  return 0;
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}