test/min_cost_arborescence_test.cc
author Peter Kovacs <kpeter@inf.elte.hu>
Fri, 17 Apr 2009 18:04:36 +0200
changeset 609 e6927fe719e6
child 625 029a48052c67
permissions -rw-r--r--
Support >= and <= constraints in NetworkSimplex (#219, #234)

By default the same inequality constraints are supported as by
Circulation (the GEQ form), but the LEQ form can also be selected
using the problemType() function.

The documentation of the min. cost flow module is reworked and
extended with important notes and explanations about the different
variants of the problem and about the dual solution and optimality
conditions.
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #include <iostream>
    20 #include <set>
    21 #include <vector>
    22 #include <iterator>
    23 
    24 #include <lemon/smart_graph.h>
    25 #include <lemon/min_cost_arborescence.h>
    26 #include <lemon/lgf_reader.h>
    27 
    28 #include "test_tools.h"
    29 
    30 using namespace lemon;
    31 using namespace std;
    32 
    33 const char test_lgf[] =
    34   "@nodes\n"
    35   "label\n"
    36   "0\n"
    37   "1\n"
    38   "2\n"
    39   "3\n"
    40   "4\n"
    41   "5\n"
    42   "6\n"
    43   "7\n"
    44   "8\n"
    45   "9\n"
    46   "@arcs\n"
    47   "     label  cost\n"
    48   "1 8  0      107\n"
    49   "0 3  1      70\n"
    50   "2 1  2      46\n"
    51   "4 1  3      28\n"
    52   "4 4  4      91\n"
    53   "3 9  5      76\n"
    54   "9 8  6      61\n"
    55   "8 1  7      39\n"
    56   "9 8  8      74\n"
    57   "8 0  9      39\n"
    58   "4 3  10     45\n"
    59   "2 2  11     34\n"
    60   "0 1  12     100\n"
    61   "6 3  13     95\n"
    62   "4 1  14     22\n"
    63   "1 1  15     31\n"
    64   "7 2  16     51\n"
    65   "2 6  17     29\n"
    66   "8 3  18     115\n"
    67   "6 9  19     32\n"
    68   "1 1  20     60\n"
    69   "0 3  21     40\n"
    70   "@attributes\n"
    71   "source 0\n";
    72 
    73 int main() {
    74   typedef SmartDigraph Digraph;
    75   DIGRAPH_TYPEDEFS(Digraph);
    76 
    77   typedef Digraph::ArcMap<double> CostMap;
    78 
    79   Digraph digraph;
    80   CostMap cost(digraph);
    81   Node source;
    82 
    83   std::istringstream is(test_lgf);
    84   digraphReader(digraph, is).
    85     arcMap("cost", cost).
    86     node("source", source).run();
    87 
    88   MinCostArborescence<Digraph, CostMap> mca(digraph, cost);
    89   mca.run(source);
    90 
    91   vector<pair<double, set<Node> > > dualSolution(mca.dualNum());
    92 
    93   for (int i = 0; i < mca.dualNum(); ++i) {
    94     dualSolution[i].first = mca.dualValue(i);
    95     for (MinCostArborescence<Digraph, CostMap>::DualIt it(mca, i);
    96          it != INVALID; ++it) {
    97       dualSolution[i].second.insert(it);
    98     }
    99   }
   100 
   101   for (ArcIt it(digraph); it != INVALID; ++it) {
   102     if (mca.reached(digraph.source(it))) {
   103       double sum = 0.0;
   104       for (int i = 0; i < int(dualSolution.size()); ++i) {
   105         if (dualSolution[i].second.find(digraph.target(it))
   106             != dualSolution[i].second.end() &&
   107             dualSolution[i].second.find(digraph.source(it))
   108             == dualSolution[i].second.end()) {
   109           sum += dualSolution[i].first;
   110         }
   111       }
   112       if (mca.arborescence(it)) {
   113         check(sum == cost[it], "INVALID DUAL");
   114       }
   115       check(sum <= cost[it], "INVALID DUAL");
   116     }
   117   }
   118 
   119 
   120   check(mca.dualValue() == mca.arborescenceValue(), "INVALID DUAL");
   121 
   122   check(mca.reached(source), "INVALID ARBORESCENCE");
   123   for (ArcIt a(digraph); a != INVALID; ++a) {
   124     check(!mca.reached(digraph.source(a)) ||
   125           mca.reached(digraph.target(a)), "INVALID ARBORESCENCE");
   126   }
   127 
   128   for (NodeIt n(digraph); n != INVALID; ++n) {
   129     if (!mca.reached(n)) continue;
   130     int cnt = 0;
   131     for (InArcIt a(digraph, n); a != INVALID; ++a) {
   132       if (mca.arborescence(a)) {
   133         check(mca.pred(n) == a, "INVALID ARBORESCENCE");
   134         ++cnt;
   135       }
   136     }
   137     check((n == source ? cnt == 0 : cnt == 1), "INVALID ARBORESCENCE");
   138   }
   139 
   140   Digraph::ArcMap<bool> arborescence(digraph);
   141   check(mca.arborescenceValue() ==
   142         minCostArborescence(digraph, cost, source, arborescence),
   143         "WRONG FUNCTION");
   144 
   145   return 0;
   146 }