/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */ /* * Main authors: * Christian Schulte * * Copyright: * Christian Schulte, 2004 * * Last modified: * $Date: 2010-10-07 20:52:01 +1100 (Thu, 07 Oct 2010) $ by $Author: schulte $ * $Revision: 11473 $ * * This file is part of Gecode, the generic constraint * development environment: * http://www.gecode.org * * Permission is hereby granted, free of charge, to any person obtaining * a copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sublicense, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. * */ #include #include using namespace Gecode; /** * \name %Graph specification for graph coloring * * The edges are described by an array of integers with even number * of elements, terminated by the elements -1,-1. * The cliques are described by an array of integers, where the first * integer gives the size of the clique, the following elements are * nodes for each clique. The cliques are terminated by -1 for clique size * * \relates GraphColor */ //@{ /// %Graph specification class GraphColorSpec { public: const int n_v; ///< Number of nodes const int* e; ///< Edges const int* c; ///< Cliques GraphColorSpec(const int n_v0, const int* e0, const int* c0) : n_v(n_v0), e(e0), c(c0) {} }; /// First example graph: edges const int g1_e[] = { 160,184, 192,199, 0,129, 20,80, 8,29, 93,171, 101,165, 124,193, 2,100, 66,173, 151,191, 164,187, 3,130, 118,176, 121,184, 25,106, 159,193, 121,123, 5,62, 97,101, 6,143, 123,163, 19,125, 17,108, 122,168, 181,184, 25,41, 62,70, 29,103, 48,67, 46,160, 79,170, 143,152, 38,184, 2,40, 191,195, 7,196, 62,199, 76,141, 82,166, 36,80, 51,189, 13,97, 3,192, 90,180, 47,176, 13,172, 92,121, 50,64, 65,113, 108,123, 26,106, 34,153, 90,123, 34,39, 116,178, 22,179, 50,61, 84,105, 84,93, 19,108, 29,59, 63,185, 119,129, 50,177, 80,194, 13,36, 46,56, 38,144, 82,193, 72,93, 49,95, 42,155, 117,140, 109,189, 19,35, 31,125, 118,191, 163,169, 40,167, 91,127, 3,121, 124,149, 40,174, 30,175, 19,132, 18,165, 34,93, 37,63, 10,55, 88,95, 76,122, 7,91, 25,141, 29,173, 139,173, 8,130, 110,158, 81,174, 113,114, 95,182, 136,149, 5,199, 56,106, 36,120, 133,187, 111,172, 19,34, 96,197, 32,108, 27,63, 50,188, 20,116, 50,118, 10,50, 24,172, 86,138, 35,50, 141,153, 98,132, 70,143, 1,97, 8,160, 37,170, 4,73, 1,94, 88,146, 59,61, 104,156, 62,172, 117,139, 66,189, 33,134, 122,169, 95,163, 95,152, 83,140, 110,189, 147,159, 22,147, 59,173, 30,41, 33,183, 181,187, 88,105, 93,151, 6,130, 24,30, 84,130, 72,120, 118,159, 147,189, 122,149, 24,175, 39,169, 164,186, 93,187, 13,156, 119,176, 73,91, 174,178, 71,198, 10,134, 30,101, 79,93, 180,187, 1,50, 51,59, 18,169, 73,153, 1,198, 137,154, 61,106, 80,113, 48,142, 100,111, 97,133, 82,97, 136,170, 53,134, 65,177, 7,80, 73,137, 6,70, 115,166, 72,196, 40,109, 91,101, 2,177, 120,185, 55,65, 72,166, 104,165, 173,187, 54,71, 3,61, 52,56, 120,149, 64,72, 42,43, 75,185, 62,68, 108,147, 30,111, 25,58, 39,93, 75,117, 61,194, 140,153, 80,121, 93,102, 9,177, 7,163, 17,70, 5,168, 63,178, 74,160, 148,158, 9,84, 30,76, 63,80, 68,99, 20,152, 7,182, 7,22, 71,134, 32,100, 107,164, 23,62, 5,98, 130,192, 65,144, 139,161, 24,124, 31,47, 29,140, 61,153, 53,109, 20,26, 143,160, 47,195, 171,172, 185,193, 128,173, 38,96, 14,171, 176,199, 111,139, 21,54, 80,171, 116,185, 184,199, 37,88, 62,133, 3,150, 48,109, 46,176, 24,178, 59,172, 180,198, 64,109, 110,111, 101,146, 66,164, 5,117, 144,179, 71,126, 166,169, 107,151, 46,85, 106,139, 27,153, 97,148, 68,185, 17,179, 10,142, 168,169, 4,46, 113,152, 52,176, 6,38, 22,48, 20,120, 2,84, 71,85, 91,116, 0,189, 116,197, 142,147, 33,165, 86,198, 146,149, 152,187, 44,62, 48,175, 56,150, 63,161, 71,164, 17,171, 19,66, -1,-1}; /// First example graph: cliques const int g1_c[] = { 30, 6,11,14,25,40,42,48,53,61,76,80,87,89,92,108,115,120,131,132,137,145,159,162,163,164,168,172,173,176,182, 30, 3,15,16,31,34,35,37,38,49,58,67,78,86,91,100,110,114,123,129,132,133,140,143,154,167,168,174,175,193,197, 25, 3,10,33,38,43,45,48,51,65,66,82,88,90,93,94,103,107,128,131,141,152,155,168,185,199, 25, 0,4,7,26,28,33,36,58,61,72,79,81,90,99,105,114,115,124,135,152,159,161,173,181,192, 25, 12,15,28,39,43,44,45,66,83,84,85,99,102,108,112,115,120,126,131,152,157,163,171,182,183, 25, 13,14,15,38,55,66,76,78,87,91,95,99,109,110,125,130,134,137,148,153,159,169,181,185,195, 25, 3,4,31,35,41,42,57,60,65,66,72,74,84,86,90,91,94,96,110,139,140,141,165,179,199, 25, 0,4,5,9,28,31,42,49,54,63,65,72,74,75,76,82,91,99,107,109,140,147,154,169,182, 25, 4,5,10,17,41,43,48,58,65,85,92,97,107,112,114,129,131,146,150,153,158,169,176,184,191, 25, 4,8,15,16,20,21,37,55,68,84,87,104,109,112,117,119,122,123,126,133,142,164,167,180,195, 25, 5,6,10,11,28,30,43,46,53,60,66,79,82,105,114,116,119,124,127,147,157,171,184,195,196, 20, 15,16,30,35,36,56,66,78,81,84,99,126,128,129,138,151,152,153,166,190, 20, 5,21,23,29,39,40,49,69,88,114,122,127,128,142,148,155,161,171,188,190, 20, 0,3,15,23,31,41,57,60,69,76,89,107,109,128,153,155,161,169,174,183, 20, 9,33,43,61,64,69,85,98,100,101,114,120,138,144,172,182,184,187,188,198, 20, 4,6,8,10,23,27,45,57,66,68,71,93,110,122,139,146,150,155,156,188, 20, 4,14,18,22,63,77,78,83,94,98,104,114,150,166,172,177,183,186,196,199, 20, 22,35,46,47,63,64,70,78,87,99,102,112,116,119,125,131,152,165,174,186, 20, 1,3,13,15,19,26,46,51,65,73,76,110,114,149,152,163,166,170,178,186, 20, 9,29,33,40,50,54,102,105,111,112,119,120,124,128,136,138,144,175,190,199, 20, 39,75,79,102,106,112,123,125,138,145,154,155,159,162,165,168,175,181,189,196, 20, 0,11,12,23,42,63,68,71,79,83,89,98,113,117,121,141,156,176,177,193, 20, 10,17,31,56,77,89,102,115,116,117,118,120,136,157,163,168,172,182,193,196, 20, 9,34,35,43,44,57,60,64,79,87,88,94,103,133,156,157,166,171,174,189, 20, 13,21,22,31,41,45,66,67,79,86,112,116,119,146,160,171,175,181,192,195, 20, 11,24,26,45,57,91,99,102,122,123,135,141,144,146,154,156,167,191,194,199, 15, 17,44,53,61,82,90,95,103,107,122,124,145,169,186,190, 15, 2,14,26,37,58,61,75,95,103,109,115,116,141,154,199, 15, 5,13,21,28,61,64,65,73,105,115,119,132,148,154,185, 15, 10,20,38,45,61,75,109,111,115,143,150,157,163,179,186, 15, 9,45,48,49,51,52,57,64,70,128,158,163,182,183,192, 15, 47,55,57,64,79,80,105,131,152,163,172,180,186,190,197, 15, 16,36,69,84,99,113,118,121,126,137,160,162,165,177,196, 15, 16,44,50,53,54,65,69,80,96,112,125,139,150,153,193, 15, 6,54,72,76,86,95,96,144,145,148,151,164,168,180,183, 15, 10,18,19,37,65,85,90,104,112,128,147,158,164,192,198, 15, 20,21,36,50,53,74,90,96,99,124,129,140,163,171,183, 15, 13,20,27,53,65,77,86,98,110,125,133,139,147,188,196, 15, 23,41,43,49,58,74,77,86,111,126,150,168,173,185,189, 15, 11,35,62,89,125,132,134,141,149,163,166,167,171,194,196, 15, 14,28,30,52,114,115,122,125,132,135,172,177,179,181,195, 15, 0,8,9,20,23,53,77,93,121,136,141,147,150,191,199, 15, 3,21,47,49,91,102,106,113,124,136,140,143,177,178,194, 15, 44,46,52,53,68,82,89,90,120,128,144,147,175,178,192, 15, 8,16,19,21,67,72,79,82,86,90,115,116,149,152,199, 15, 12,30,78,80,97,120,122,123,143,146,151,165,173,177,178, 15, 9,19,39,46,91,109,128,130,131,146,148,150,178,185,198, 10, 29,44,69,74,96,115,122,126,189,199, 10, 22,42,52,53,97,113,146,151,160,195, 10, 19,20,32,77,81,133,134,138,147,177, 10, 0,4,56,59,107,109,144,149,158,167, 10, 6,69,99,104,110,114,118,134,152,172, 5, 25,76,126,140,143, 5, 4,54,67,116,142, 5, 47,52,124,151,192, 5, 32,55,61,64,73, 5, 11,65,128,134,190, 5, 45,48,63,131,139, 5, 34,55,82,108,151, 5, 24,34,54,112,156, 5, 12,47,72,148,163, 5, 74,126,145,162,170, 5, 73,78,104,175,192, 5, 19,83,127,130,166, 5, 20,90,98,137,165, 5, 22,24,29,49,132, 5, 82,92,116,134,184, -1}; /// First example graph const GraphColorSpec g1(200, g1_e, g1_c); /// Second example graph: edges const int g2_e[] = { 63,97, 67,85, 18,180, 2,143, 55,156, 28,105, 37,196, 26,33, 88,199, 175,179, 45,46, 62,70, 53,58, 49,177, 91,178, 52,129, 147,165, 83,95, 68,172, 66,150, 7,112, 71,92, 97,150, 114,116, 56,86, 154,188, 95,97, 159,199, 68,119, 11,81, 79,116, 64,74, 88,89, 99,114, 70,73, 87,162, 24,119, 9,25, 174,188, 11,80, 47,198, 86,145, 7,70, 37,170, 138,180, 66,199, 98,153, 70,142, 84,196, 78,185, 7,131, 54,76, 69,82, 53,166, 25,178, 3,36, 128,197, 59,96, 122,137, 54,124, 157,162, 3,146, 72,198, 2,94, 137,158, 64,131, 2,79, 18,119, 22,38, 92,136, 7,108, 179,194, 68,166, 10,84, 28,192, 103,104, 28,75, 8,43, 153,164, 59,119, 88,177, 36,70, 59,154, 57,75, 109,174, 155,184, 16,74, 99,148, 77,121, 54,177, 38,172, 138,174, 7,16, 28,146, 18,192, 4,154, 17,31, 56,57, 174,177, 81,122, 101,175, 21,155, 48,96, 124,154, 129,130, 58,169, 19,57, 115,165, 40,117, 34,181, 28,32, 32,176, 19,119, 20,93, 137,172, 55,135, 92,95, 34,51, 5,81, 63,118, 72,94, 157,181, 15,68, 41,90, 35,73, 159,183, 115,128, 28,183, 34,45, 149,177, 74,137, 51,110, 25,170, 43,123, 53,109, 4,26, 68,80, 53,171, 48,159, 0,28, 67,176, 87,163, 75,165, 137,162, 150,199, 57,153, 32,93, 25,92, 13,88, 115,167, 16,192, 113,157, 90,125, 104,188, 148,171, 96,101, 22,68, 25,62, 89,161, 24,158, 66,190, 31,34, 106,133, 51,102, 146,163, 31,154, 56,129, 66,157, 38,93, 73,166, 117,174, 93,161, 3,95, 86,181, 131,139, 5,182, 30,66, 0,11, 88,107, 54,101, 36,66, 25,176, 8,38, 31,177, 78,195, 122,179, 42,60, 83,112, 149,161, 184,188, 65,126, 74,198, 38,80, 135,172, 43,156, 148,151, 135,195, 111,184, 10,14, 97,152, -1,-1}; /// Second example graph: cliques const int g2_c[] = { 30, 10,11,17,20,24,29,33,40,45,50,51,76,77,85,88,101,114,120,122,127,129,136,144,147,148,157,169,180,184,193, 30, 0,2,14,21,38,40,44,51,72,82,91,99,106,109,119,123,126,136,141,154,157,161,163,165,166,171,175,182,183,196, 30, 2,17,20,30,35,36,37,39,46,56,61,72,75,77,80,84,85,96,97,100,107,112,123,156,160,163,175,181,182,195, 25, 11,19,36,41,44,59,60,73,74,89,93,94,108,109,113,130,132,153,163,167,182,186,193,196,199, 25, 2,11,25,30,31,41,49,51,52,53,85,86,93,101,105,108,111,130,135,144,150,183,185,191,194, 25, 1,6,9,11,12,13,19,21,33,49,51,77,124,128,130,131,140,146,147,161,171,180,181,185,198, 25, 3,5,31,39,42,57,59,61,90,93,98,102,106,121,129,132,140,160,165,166,168,185,187,193,194, 25, 9,12,16,23,33,41,44,61,68,73,85,93,96,113,118,122,125,127,129,133,139,146,181,186,199, 25, 6,23,35,42,45,57,65,67,70,77,80,96,100,105,114,119,129,145,146,152,157,160,166,190,195, 25, 8,18,19,27,36,40,49,52,60,65,75,84,85,96,97,107,109,110,120,122,132,154,155,172,189, 25, 1,25,27,37,39,45,56,61,69,70,80,87,89,102,111,115,120,126,134,146,156,169,173,175,192, 20, 8,14,20,21,32,39,50,55,88,91,102,120,126,142,159,165,171,175,184,186, 20, 10,15,35,43,50,52,60,77,80,81,85,87,106,120,145,151,155,159,176,196, 20, 10,17,20,33,46,55,60,68,95,96,103,112,117,118,120,123,127,141,147,179, 20, 9,34,41,52,56,72,73,100,102,116,124,131,138,155,157,158,172,173,182,183, 20, 0,14,16,27,29,44,70,95,101,104,115,127,140,158,161,168,170,173,181,189, 20, 6,14,17,18,23,27,50,51,83,84,93,107,108,116,122,136,154,159,172,185, 20, 11,16,17,21,32,38,45,49,55,56,84,88,102,123,126,133,173,189,195,198, 20, 0,14,21,29,30,40,63,67,93,98,116,122,131,140,150,152,174,178,183,190, 20, 8,14,28,36,44,65,72,79,84,111,114,124,130,134,140,158,182,185,193,197, 20, 9,10,12,17,28,42,46,50,57,62,90,117,132,149,168,176,178,182,187,188, 20, 2,4,22,27,31,32,65,74,108,117,132,142,153,159,160,178,180,187,192,195, 20, 2,4,7,21,56,64,67,100,103,130,135,140,147,151,156,161,167,191,193,196, 20, 6,18,24,30,50,51,67,82,84,88,93,95,106,113,138,146,168,187,190,198, 20, 28,37,44,98,99,107,112,119,129,132,135,151,156,167,168,179,182,190,198,199, 15, 4,37,61,64,67,77,93,103,105,118,136,159,169,177,193, 15, 17,44,53,61,82,90,95,103,107,122,124,145,169,186,190, 15, 21,54,80,100,110,120,126,127,132,142,149,150,162,181,186, 15, 3,7,21,22,40,41,82,94,96,98,126,140,143,147,152, 15, 4,14,58,66,80,100,107,111,126,133,140,141,148,155,167, 15, 31,38,44,48,59,74,75,77,100,105,139,168,171,182,187, 15, 0,5,55,62,66,67,74,84,92,128,160,163,188,189,195, 15, 0,36,55,73,80,96,121,133,167,173,190,191,193,195,198, 15, 21,33,41,43,52,62,69,77,88,110,114,118,139,142,187, 15, 12,14,23,29,44,58,67,74,124,149,150,156,167,171,183, 15, 22,33,36,48,60,63,90,92,107,108,137,140,144,165,193, 15, 11,24,40,45,49,59,72,123,125,132,151,161,167,179,184, 15, 4,19,20,48,61,76,98,106,136,147,155,177,183,191,192, 15, 17,22,28,35,55,74,86,90,98,106,121,138,168,190,195, 15, 24,30,35,44,55,63,80,120,128,130,148,160,163,166,192, 15, 20,30,59,64,69,94,104,106,139,140,144,147,156,161,199, 15, 13,30,38,49,54,61,86,95,103,105,131,148,156,162,180, 15, 2,25,34,41,46,63,69,81,91,113,139,159,186,188,190, 15, 1,6,14,35,47,50,66,81,90,136,137,152,156,168,195, 15, 34,37,47,52,94,100,104,105,107,131,147,171,186,191,192, 15, 9,14,29,37,109,125,137,142,145,147,151,159,167,178,192, 15, 13,45,60,62,78,99,104,118,142,143,156,179,189,191,197, 15, 3,15,23,33,66,71,82,89,99,110,113,135,143,158,171, 15, 27,39,101,102,118,133,134,138,141,144,145,148,165,169,189, 15, 12,18,20,36,50,51,53,76,86,120,141,176,178,186,198, 10, 6,8,17,77,109,112,115,124,129,193, 10, 21,31,51,58,86,112,117,126,127,143, 10, 10,74,87,108,123,134,157,180,186,190, 10, 13,14,15,44,67,118,133,142,146,193, 10, 40,44,46,66,73,128,141,161,174,192, 5, 25,117,163,165,192, 5, 40,46,105,121,134, 5, 3,12,56,90,126, 5, 13,95,98,120,188, 5, 3,98,111,128,194, 5, 4,21,51,65,73, 5, 36,106,124,132,197, 5, 5,35,57,91,144, 5, 0,19,122,177,190, 5, 85,98,111,113,134, 5, 49,85,107,139,149, 5, 54,88,102,111,172, 5, 41,74,115,170,184, 5, 33,70,123,151,159, 5, 50,82,117,123,163, -1}; /// Second example graph const GraphColorSpec g2(200, g2_e, g2_c); //@} /** * \brief %Example: Clique-based graph coloring * * \ingroup Example * */ class GraphColor : public MinimizeScript { private: const GraphColorSpec& g; /// Color of nodes IntVarArray v; /// Number of colors IntVar m; public: /// Model variants enum { MODEL_NONE, ///< No lower bound MODEL_CLIQUE ///< Use maximal clique size as lower bound }; /// Branching to use for model enum { BRANCH_DEGREE, ///< Choose variable with largest degree BRANCH_SIZE, ///< Choose variable with smallest size BRANCH_SIZE_DEGREE, ///< Choose variable with smallest size/degree BRANCH_SIZE_AFC, ///< Choose variable with smallest size/degree }; /// The actual model GraphColor(const SizeOptions& opt) : g(opt.size() == 1 ? g2 : g1), v(*this,g.n_v,0,g.n_v), m(*this,0,g.n_v) { rel(*this, v, IRT_LQ, m); for (int i = 0; g.e[i] != -1; i += 2) rel(*this, v[g.e[i]], IRT_NQ, v[g.e[i+1]]); const int* c = g.c; for (int i = *c++; i--; c++) rel(*this, v[*c], IRT_EQ, i); while (*c != -1) { int n = *c; IntVarArgs x(n); c++; for (int i = n; i--; c++) x[i] = v[*c]; distinct(*this, x, opt.icl()); if (opt.model() == MODEL_CLIQUE) rel(*this, m, IRT_GQ, n-1); } branch(*this, m, INT_VAL_MIN); switch (opt.branching()) { case BRANCH_SIZE: branch(*this, v, INT_VAR_SIZE_MIN, INT_VAL_MIN); break; case BRANCH_DEGREE: branch(*this, v, tiebreak(INT_VAR_DEGREE_MAX,INT_VAR_SIZE_MIN), INT_VAL_MIN); break; case BRANCH_SIZE_DEGREE: branch(*this, v, INT_VAR_SIZE_DEGREE_MIN, INT_VAL_MIN); break; case BRANCH_SIZE_AFC: branch(*this, v, INT_VAR_SIZE_AFC_MIN, INT_VAL_MIN); break; default: break; } } /// Cost function virtual IntVar cost(void) const { return m; } /// Constructor for cloning \a s GraphColor(bool share, GraphColor& s) : MinimizeScript(share,s), g(s.g) { v.update(*this, share, s.v); m.update(*this, share, s.m); } /// Copying during cloning virtual Space* copy(bool share) { return new GraphColor(share,*this); } /// Print the solution virtual void print(std::ostream& os) const { os << "\tm = " << m << std::endl << "\tv[] = {"; for (int i = 0; i < v.size(); i++) { os << v[i] << ", "; if ((i+1) % 15 == 0) os << std::endl << "\t "; } os << "};" << std::endl; } }; /** \brief Main-function * \relates GraphColor */ int main(int argc, char* argv[]) { SizeOptions opt("GraphColor"); opt.icl(ICL_DOM); opt.iterations(20); opt.solutions(0); opt.model(GraphColor::MODEL_NONE); opt.model(GraphColor::MODEL_NONE, "none", "no lower bound"); opt.model(GraphColor::MODEL_CLIQUE, "clique", "use maximal clique size as lower bound"); opt.branching(GraphColor::BRANCH_DEGREE); opt.branching(GraphColor::BRANCH_DEGREE, "degree"); opt.branching(GraphColor::BRANCH_SIZE, "size"); opt.branching(GraphColor::BRANCH_SIZE_DEGREE, "sizedegree"); opt.branching(GraphColor::BRANCH_SIZE_AFC, "sizeafc"); opt.parse(argc,argv); Script::run(opt); return 0; } // STATISTICS: example-any