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+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2013
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#include <iostream>
+#include <fstream>
+#include <limits>
+
+#include <lemon/list_graph.h>
+#include <lemon/lgf_reader.h>
+
+#include <lemon/network_simplex.h>
+#include <lemon/capacity_scaling.h>
+#include <lemon/cost_scaling.h>
+#include <lemon/cycle_canceling.h>
+
+#include <lemon/concepts/digraph.h>
+#include <lemon/concepts/heap.h>
+#include <lemon/concept_check.h>
+
+#include "test_tools.h"
+
+using namespace lemon;
+
+// Test networks
+char test_lgf[] =
+ "@nodes\n"
+ "label sup1 sup2 sup3 sup4 sup5 sup6\n"
+ " 1 20 27 0 30 20 30\n"
+ " 2 -4 0 0 0 -8 -3\n"
+ " 3 0 0 0 0 0 0\n"
+ " 4 0 0 0 0 0 0\n"
+ " 5 9 0 0 0 6 11\n"
+ " 6 -6 0 0 0 -5 -6\n"
+ " 7 0 0 0 0 0 0\n"
+ " 8 0 0 0 0 0 3\n"
+ " 9 3 0 0 0 0 0\n"
+ " 10 -2 0 0 0 -7 -2\n"
+ " 11 0 0 0 0 -10 0\n"
+ " 12 -20 -27 0 -30 -30 -20\n"
+ "\n"
+ "@arcs\n"
+ " cost cap low1 low2 low3\n"
+ " 1 2 70 11 0 8 8\n"
+ " 1 3 150 3 0 1 0\n"
+ " 1 4 80 15 0 2 2\n"
+ " 2 8 80 12 0 0 0\n"
+ " 3 5 140 5 0 3 1\n"
+ " 4 6 60 10 0 1 0\n"
+ " 4 7 80 2 0 0 0\n"
+ " 4 8 110 3 0 0 0\n"
+ " 5 7 60 14 0 0 0\n"
+ " 5 11 120 12 0 0 0\n"
+ " 6 3 0 3 0 0 0\n"
+ " 6 9 140 4 0 0 0\n"
+ " 6 10 90 8 0 0 0\n"
+ " 7 1 30 5 0 0 -5\n"
+ " 8 12 60 16 0 4 3\n"
+ " 9 12 50 6 0 0 0\n"
+ "10 12 70 13 0 5 2\n"
+ "10 2 100 7 0 0 0\n"
+ "10 7 60 10 0 0 -3\n"
+ "11 10 20 14 0 6 -20\n"
+ "12 11 30 10 0 0 -10\n"
+ "\n"
+ "@attributes\n"
+ "source 1\n"
+ "target 12\n";
+
+char test_neg1_lgf[] =
+ "@nodes\n"
+ "label sup\n"
+ " 1 100\n"
+ " 2 0\n"
+ " 3 0\n"
+ " 4 -100\n"
+ " 5 0\n"
+ " 6 0\n"
+ " 7 0\n"
+ "@arcs\n"
+ " cost low1 low2\n"
+ "1 2 100 0 0\n"
+ "1 3 30 0 0\n"
+ "2 4 20 0 0\n"
+ "3 4 80 0 0\n"
+ "3 2 50 0 0\n"
+ "5 3 10 0 0\n"
+ "5 6 80 0 1000\n"
+ "6 7 30 0 -1000\n"
+ "7 5 -120 0 0\n";
+
+char test_neg2_lgf[] =
+ "@nodes\n"
+ "label sup\n"
+ " 1 100\n"
+ " 2 -300\n"
+ "@arcs\n"
+ " cost\n"
+ "1 2 -1\n";
+
+
+// Test data
+typedef ListDigraph Digraph;
+DIGRAPH_TYPEDEFS(ListDigraph);
+
+Digraph gr;
+Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), l3(gr), u(gr);
+Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr), s4(gr), s5(gr), s6(gr);
+ConstMap<Arc, int> cc(1), cu(std::numeric_limits<int>::max());
+Node v, w;
+
+Digraph neg1_gr;
+Digraph::ArcMap<int> neg1_c(neg1_gr), neg1_l1(neg1_gr), neg1_l2(neg1_gr);
+ConstMap<Arc, int> neg1_u1(std::numeric_limits<int>::max()), neg1_u2(5000);
+Digraph::NodeMap<int> neg1_s(neg1_gr);
+
+Digraph neg2_gr;
+Digraph::ArcMap<int> neg2_c(neg2_gr);
+ConstMap<Arc, int> neg2_l(0), neg2_u(1000);
+Digraph::NodeMap<int> neg2_s(neg2_gr);
+
+
+enum SupplyType {
+ EQ,
+ GEQ,
+ LEQ
+};
+
+
+// Check the interface of an MCF algorithm
+template <typename GR, typename Value, typename Cost>
+class McfClassConcept
+{
+public:
+
+ template <typename MCF>
+ struct Constraints {
+ void constraints() {
+ checkConcept<concepts::Digraph, GR>();
+
+ const Constraints& me = *this;
+
+ MCF mcf(me.g);
+ const MCF& const_mcf = mcf;
+
+ b = mcf.reset().resetParams()
+ .lowerMap(me.lower)
+ .upperMap(me.upper)
+ .costMap(me.cost)
+ .supplyMap(me.sup)
+ .stSupply(me.n, me.n, me.k)
+ .run();
+
+ c = const_mcf.totalCost();
+ x = const_mcf.template totalCost<double>();
+ v = const_mcf.flow(me.a);
+ c = const_mcf.potential(me.n);
+ const_mcf.flowMap(fm);
+ const_mcf.potentialMap(pm);
+ }
+
+ typedef typename GR::Node Node;
+ typedef typename GR::Arc Arc;
+ typedef concepts::ReadMap<Node, Value> NM;
+ typedef concepts::ReadMap<Arc, Value> VAM;
+ typedef concepts::ReadMap<Arc, Cost> CAM;
+ typedef concepts::WriteMap<Arc, Value> FlowMap;
+ typedef concepts::WriteMap<Node, Cost> PotMap;
+
+ GR g;
+ VAM lower;
+ VAM upper;
+ CAM cost;
+ NM sup;
+ Node n;
+ Arc a;
+ Value k;
+
+ FlowMap fm;
+ PotMap pm;
+ bool b;
+ double x;
+ typename MCF::Value v;
+ typename MCF::Cost c;
+ };
+
+};
+
+
+// Check the feasibility of the given flow (primal soluiton)
+template < typename GR, typename LM, typename UM,
+ typename SM, typename FM >
+bool checkFlow( const GR& gr, const LM& lower, const UM& upper,
+ const SM& supply, const FM& flow,
+ SupplyType type = EQ )
+{
+ TEMPLATE_DIGRAPH_TYPEDEFS(GR);
+
+ for (ArcIt e(gr); e != INVALID; ++e) {
+ if (flow[e] < lower[e] || flow[e] > upper[e]) return false;
+ }
+
+ for (NodeIt n(gr); n != INVALID; ++n) {
+ typename SM::Value sum = 0;
+ for (OutArcIt e(gr, n); e != INVALID; ++e)
+ sum += flow[e];
+ for (InArcIt e(gr, n); e != INVALID; ++e)
+ sum -= flow[e];
+ bool b = (type == EQ && sum == supply[n]) ||
+ (type == GEQ && sum >= supply[n]) ||
+ (type == LEQ && sum <= supply[n]);
+ if (!b) return false;
+ }
+
+ return true;
+}
+
+// Check the feasibility of the given potentials (dual soluiton)
+// using the "Complementary Slackness" optimality condition
+template < typename GR, typename LM, typename UM,
+ typename CM, typename SM, typename FM, typename PM >
+bool checkPotential( const GR& gr, const LM& lower, const UM& upper,
+ const CM& cost, const SM& supply, const FM& flow,
+ const PM& pi, SupplyType type )
+{
+ TEMPLATE_DIGRAPH_TYPEDEFS(GR);
+
+ bool opt = true;
+ for (ArcIt e(gr); opt && e != INVALID; ++e) {
+ typename CM::Value red_cost =
+ cost[e] + pi[gr.source(e)] - pi[gr.target(e)];
+ opt = red_cost == 0 ||
+ (red_cost > 0 && flow[e] == lower[e]) ||
+ (red_cost < 0 && flow[e] == upper[e]);
+ }
+
+ for (NodeIt n(gr); opt && n != INVALID; ++n) {
+ typename SM::Value sum = 0;
+ for (OutArcIt e(gr, n); e != INVALID; ++e)
+ sum += flow[e];
+ for (InArcIt e(gr, n); e != INVALID; ++e)
+ sum -= flow[e];
+ if (type != LEQ) {
+ opt = (pi[n] <= 0) && (sum == supply[n] || pi[n] == 0);
+ } else {
+ opt = (pi[n] >= 0) && (sum == supply[n] || pi[n] == 0);
+ }
+ }
+
+ return opt;
+}
+
+// Check whether the dual cost is equal to the primal cost
+template < typename GR, typename LM, typename UM,
+ typename CM, typename SM, typename PM >
+bool checkDualCost( const GR& gr, const LM& lower, const UM& upper,
+ const CM& cost, const SM& supply, const PM& pi,
+ typename CM::Value total )
+{
+ TEMPLATE_DIGRAPH_TYPEDEFS(GR);
+
+ typename CM::Value dual_cost = 0;
+ SM red_supply(gr);
+ for (NodeIt n(gr); n != INVALID; ++n) {
+ red_supply[n] = supply[n];
+ }
+ for (ArcIt a(gr); a != INVALID; ++a) {
+ if (lower[a] != 0) {
+ dual_cost += lower[a] * cost[a];
+ red_supply[gr.source(a)] -= lower[a];
+ red_supply[gr.target(a)] += lower[a];
+ }
+ }
+
+ for (NodeIt n(gr); n != INVALID; ++n) {
+ dual_cost -= red_supply[n] * pi[n];
+ }
+ for (ArcIt a(gr); a != INVALID; ++a) {
+ typename CM::Value red_cost =
+ cost[a] + pi[gr.source(a)] - pi[gr.target(a)];
+ dual_cost -= (upper[a] - lower[a]) * std::max(-red_cost, 0);
+ }
+
+ return dual_cost == total;
+}
+
+// Run a minimum cost flow algorithm and check the results
+template < typename MCF, typename GR,
+ typename LM, typename UM,
+ typename CM, typename SM,
+ typename PT >
+void checkMcf( const MCF& mcf, PT mcf_result,
+ const GR& gr, const LM& lower, const UM& upper,
+ const CM& cost, const SM& supply,
+ PT result, bool optimal, typename CM::Value total,
+ const std::string &test_id = "",
+ SupplyType type = EQ )
+{
+ check(mcf_result == result, "Wrong result " + test_id);
+ if (optimal) {
+ typename GR::template ArcMap<typename SM::Value> flow(gr);
+ typename GR::template NodeMap<typename CM::Value> pi(gr);
+ mcf.flowMap(flow);
+ mcf.potentialMap(pi);
+ check(checkFlow(gr, lower, upper, supply, flow, type),
+ "The flow is not feasible " + test_id);
+ check(mcf.totalCost() == total, "The flow is not optimal " + test_id);
+ check(checkPotential(gr, lower, upper, cost, supply, flow, pi, type),
+ "Wrong potentials " + test_id);
+ check(checkDualCost(gr, lower, upper, cost, supply, pi, total),
+ "Wrong dual cost " + test_id);
+ }
+}
+
+template < typename MCF, typename Param >
+void runMcfGeqTests( Param param,
+ const std::string &test_str = "",
+ bool full_neg_cost_support = false )
+{
+ MCF mcf1(gr), mcf2(neg1_gr), mcf3(neg2_gr);
+
+ // Basic tests
+ mcf1.upperMap(u).costMap(c).supplyMap(s1);
+ checkMcf(mcf1, mcf1.run(param), gr, l1, u, c, s1,
+ mcf1.OPTIMAL, true, 5240, test_str + "-1");
+ mcf1.stSupply(v, w, 27);
+ checkMcf(mcf1, mcf1.run(param), gr, l1, u, c, s2,
+ mcf1.OPTIMAL, true, 7620, test_str + "-2");
+ mcf1.lowerMap(l2).supplyMap(s1);
+ checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s1,
+ mcf1.OPTIMAL, true, 5970, test_str + "-3");
+ mcf1.stSupply(v, w, 27);
+ checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s2,
+ mcf1.OPTIMAL, true, 8010, test_str + "-4");
+ mcf1.resetParams().supplyMap(s1);
+ checkMcf(mcf1, mcf1.run(param), gr, l1, cu, cc, s1,
+ mcf1.OPTIMAL, true, 74, test_str + "-5");
+ mcf1.lowerMap(l2).stSupply(v, w, 27);
+ checkMcf(mcf1, mcf1.run(param), gr, l2, cu, cc, s2,
+ mcf1.OPTIMAL, true, 94, test_str + "-6");
+ mcf1.reset();
+ checkMcf(mcf1, mcf1.run(param), gr, l1, cu, cc, s3,
+ mcf1.OPTIMAL, true, 0, test_str + "-7");
+ mcf1.lowerMap(l2).upperMap(u);
+ checkMcf(mcf1, mcf1.run(param), gr, l2, u, cc, s3,
+ mcf1.INFEASIBLE, false, 0, test_str + "-8");
+ mcf1.lowerMap(l3).upperMap(u).costMap(c).supplyMap(s4);
+ checkMcf(mcf1, mcf1.run(param), gr, l3, u, c, s4,
+ mcf1.OPTIMAL, true, 6360, test_str + "-9");
+
+ // Tests for the GEQ form
+ mcf1.resetParams().upperMap(u).costMap(c).supplyMap(s5);
+ checkMcf(mcf1, mcf1.run(param), gr, l1, u, c, s5,
+ mcf1.OPTIMAL, true, 3530, test_str + "-10", GEQ);
+ mcf1.lowerMap(l2);
+ checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s5,
+ mcf1.OPTIMAL, true, 4540, test_str + "-11", GEQ);
+ mcf1.supplyMap(s6);
+ checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s6,
+ mcf1.INFEASIBLE, false, 0, test_str + "-12", GEQ);
+
+ // Tests with negative costs
+ mcf2.lowerMap(neg1_l1).costMap(neg1_c).supplyMap(neg1_s);
+ checkMcf(mcf2, mcf2.run(param), neg1_gr, neg1_l1, neg1_u1, neg1_c, neg1_s,
+ mcf2.UNBOUNDED, false, 0, test_str + "-13");
+ mcf2.upperMap(neg1_u2);
+ checkMcf(mcf2, mcf2.run(param), neg1_gr, neg1_l1, neg1_u2, neg1_c, neg1_s,
+ mcf2.OPTIMAL, true, -40000, test_str + "-14");
+ mcf2.resetParams().lowerMap(neg1_l2).costMap(neg1_c).supplyMap(neg1_s);
+ checkMcf(mcf2, mcf2.run(param), neg1_gr, neg1_l2, neg1_u1, neg1_c, neg1_s,
+ mcf2.UNBOUNDED, false, 0, test_str + "-15");
+
+ mcf3.costMap(neg2_c).supplyMap(neg2_s);
+ if (full_neg_cost_support) {
+ checkMcf(mcf3, mcf3.run(param), neg2_gr, neg2_l, neg2_u, neg2_c, neg2_s,
+ mcf3.OPTIMAL, true, -300, test_str + "-16", GEQ);
+ } else {
+ checkMcf(mcf3, mcf3.run(param), neg2_gr, neg2_l, neg2_u, neg2_c, neg2_s,
+ mcf3.UNBOUNDED, false, 0, test_str + "-17", GEQ);
+ }
+ mcf3.upperMap(neg2_u);
+ checkMcf(mcf3, mcf3.run(param), neg2_gr, neg2_l, neg2_u, neg2_c, neg2_s,
+ mcf3.OPTIMAL, true, -300, test_str + "-18", GEQ);
+
+ // Tests for empty graph
+ Digraph gr0;
+ MCF mcf0(gr0);
+ mcf0.run(param);
+ check(mcf0.totalCost() == 0, "Wrong total cost");
+}
+
+template < typename MCF, typename Param >
+void runMcfLeqTests( Param param,
+ const std::string &test_str = "" )
+{
+ // Tests for the LEQ form
+ MCF mcf1(gr);
+ mcf1.supplyType(mcf1.LEQ);
+ mcf1.upperMap(u).costMap(c).supplyMap(s6);
+ checkMcf(mcf1, mcf1.run(param), gr, l1, u, c, s6,
+ mcf1.OPTIMAL, true, 5080, test_str + "-19", LEQ);
+ mcf1.lowerMap(l2);
+ checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s6,
+ mcf1.OPTIMAL, true, 5930, test_str + "-20", LEQ);
+ mcf1.supplyMap(s5);
+ checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s5,
+ mcf1.INFEASIBLE, false, 0, test_str + "-21", LEQ);
+}
+
+
+int main()
+{
+ // Read the test networks
+ std::istringstream input(test_lgf);
+ DigraphReader<Digraph>(gr, input)
+ .arcMap("cost", c)
+ .arcMap("cap", u)
+ .arcMap("low1", l1)
+ .arcMap("low2", l2)
+ .arcMap("low3", l3)
+ .nodeMap("sup1", s1)
+ .nodeMap("sup2", s2)
+ .nodeMap("sup3", s3)
+ .nodeMap("sup4", s4)
+ .nodeMap("sup5", s5)
+ .nodeMap("sup6", s6)
+ .node("source", v)
+ .node("target", w)
+ .run();
+
+ std::istringstream neg_inp1(test_neg1_lgf);
+ DigraphReader<Digraph>(neg1_gr, neg_inp1)
+ .arcMap("cost", neg1_c)
+ .arcMap("low1", neg1_l1)
+ .arcMap("low2", neg1_l2)
+ .nodeMap("sup", neg1_s)
+ .run();
+
+ std::istringstream neg_inp2(test_neg2_lgf);
+ DigraphReader<Digraph>(neg2_gr, neg_inp2)
+ .arcMap("cost", neg2_c)
+ .nodeMap("sup", neg2_s)
+ .run();
+
+ // Check the interface of NetworkSimplex
+ {
+ typedef concepts::Digraph GR;
+ checkConcept< McfClassConcept<GR, int, int>,
+ NetworkSimplex<GR> >();
+ checkConcept< McfClassConcept<GR, double, double>,
+ NetworkSimplex<GR, double> >();
+ checkConcept< McfClassConcept<GR, int, double>,
+ NetworkSimplex<GR, int, double> >();
+ }
+
+ // Check the interface of CapacityScaling
+ {
+ typedef concepts::Digraph GR;
+ checkConcept< McfClassConcept<GR, int, int>,
+ CapacityScaling<GR> >();
+ checkConcept< McfClassConcept<GR, double, double>,
+ CapacityScaling<GR, double> >();
+ checkConcept< McfClassConcept<GR, int, double>,
+ CapacityScaling<GR, int, double> >();
+ typedef CapacityScaling<GR>::
+ SetHeap<concepts::Heap<int, RangeMap<int> > >::Create CAS;
+ checkConcept< McfClassConcept<GR, int, int>, CAS >();
+ }
+
+ // Check the interface of CostScaling
+ {
+ typedef concepts::Digraph GR;
+ checkConcept< McfClassConcept<GR, int, int>,
+ CostScaling<GR> >();
+ checkConcept< McfClassConcept<GR, double, double>,
+ CostScaling<GR, double> >();
+ checkConcept< McfClassConcept<GR, int, double>,
+ CostScaling<GR, int, double> >();
+ typedef CostScaling<GR>::
+ SetLargeCost<double>::Create COS;
+ checkConcept< McfClassConcept<GR, int, int>, COS >();
+ }
+
+ // Check the interface of CycleCanceling
+ {
+ typedef concepts::Digraph GR;
+ checkConcept< McfClassConcept<GR, int, int>,
+ CycleCanceling<GR> >();
+ checkConcept< McfClassConcept<GR, double, double>,
+ CycleCanceling<GR, double> >();
+ checkConcept< McfClassConcept<GR, int, double>,
+ CycleCanceling<GR, int, double> >();
+ }
+
+ // Test NetworkSimplex
+ {
+ typedef NetworkSimplex<Digraph> MCF;
+ runMcfGeqTests<MCF>(MCF::FIRST_ELIGIBLE, "NS-FE", true);
+ runMcfLeqTests<MCF>(MCF::FIRST_ELIGIBLE, "NS-FE");
+ runMcfGeqTests<MCF>(MCF::BEST_ELIGIBLE, "NS-BE", true);
+ runMcfLeqTests<MCF>(MCF::BEST_ELIGIBLE, "NS-BE");
+ runMcfGeqTests<MCF>(MCF::BLOCK_SEARCH, "NS-BS", true);
+ runMcfLeqTests<MCF>(MCF::BLOCK_SEARCH, "NS-BS");
+ runMcfGeqTests<MCF>(MCF::CANDIDATE_LIST, "NS-CL", true);
+ runMcfLeqTests<MCF>(MCF::CANDIDATE_LIST, "NS-CL");
+ runMcfGeqTests<MCF>(MCF::ALTERING_LIST, "NS-AL", true);
+ runMcfLeqTests<MCF>(MCF::ALTERING_LIST, "NS-AL");
+ }
+
+ // Test CapacityScaling
+ {
+ typedef CapacityScaling<Digraph> MCF;
+ runMcfGeqTests<MCF>(0, "SSP");
+ runMcfGeqTests<MCF>(2, "CAS");
+ }
+
+ // Test CostScaling
+ {
+ typedef CostScaling<Digraph> MCF;
+ runMcfGeqTests<MCF>(MCF::PUSH, "COS-PR");
+ runMcfGeqTests<MCF>(MCF::AUGMENT, "COS-AR");
+ runMcfGeqTests<MCF>(MCF::PARTIAL_AUGMENT, "COS-PAR");
+ }
+
+ // Test CycleCanceling
+ {
+ typedef CycleCanceling<Digraph> MCF;
+ runMcfGeqTests<MCF>(MCF::SIMPLE_CYCLE_CANCELING, "SCC");
+ runMcfGeqTests<MCF>(MCF::MINIMUM_MEAN_CYCLE_CANCELING, "MMCC");
+ runMcfGeqTests<MCF>(MCF::CANCEL_AND_TIGHTEN, "CAT");
+ }
+
+ return 0;
+}
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