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1 package Graph::CyclesDetection;
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2 #
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3 # $RCSfile: CyclesDetection.pm,v $
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4 # $Date: 2015/02/28 20:49:06 $
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5 # $Revision: 1.27 $
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6 #
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7 # Author: Manish Sud <msud@san.rr.com>
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8 #
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9 # Copyright (C) 2015 Manish Sud. All rights reserved.
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10 #
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11 # This file is part of MayaChemTools.
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12 #
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13 # MayaChemTools is free software; you can redistribute it and/or modify it under
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14 # the terms of the GNU Lesser General Public License as published by the Free
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15 # Software Foundation; either version 3 of the License, or (at your option) any
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16 # later version.
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17 #
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18 # MayaChemTools is distributed in the hope that it will be useful, but without
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19 # any warranty; without even the implied warranty of merchantability of fitness
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20 # for a particular purpose. See the GNU Lesser General Public License for more
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21 # details.
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22 #
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23 # You should have received a copy of the GNU Lesser General Public License
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24 # along with MayaChemTools; if not, see <http://www.gnu.org/licenses/> or
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25 # write to the Free Software Foundation Inc., 59 Temple Place, Suite 330,
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26 # Boston, MA, 02111-1307, USA.
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27 #
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28
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29 use strict;
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30 use Carp;
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31 use Exporter;
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32 use Graph;
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33 use Graph::Path;
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34 use Graph::PathGraph;
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35 use BitVector;
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36
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37 use vars qw(@ISA @EXPORT @EXPORT_OK %EXPORT_TAGS);
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38
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39 @ISA = qw(Exporter);
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40 @EXPORT = qw();
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41 @EXPORT_OK = qw();
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42
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43 %EXPORT_TAGS = (all => [@EXPORT, @EXPORT_OK]);
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44
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45 # Setup class variables...
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46 my($ClassName);
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47 _InitializeClass();
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48
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49 # Overload Perl functions...
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50 use overload '""' => 'StringifyCyclesDetection';
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51
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52 # Class constructor...
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53 sub new {
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54 my($Class, $Graph) = @_;
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55
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56 # Initialize object...
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57 my $This = {};
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58 bless $This, ref($Class) || $Class;
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59 $This->_InitializeCyclesDetection($Graph);
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60
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61 return $This;
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62 }
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63
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64 # Initialize object data...
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65 sub _InitializeCyclesDetection {
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66 my($This, $Graph) = @_;
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67
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68 $This->{Graph} = $Graph;
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69
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70 # Cycles list...
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71 @{$This->{AllCyclicPaths}} = ();
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72
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73 # Cyclic paths which are not part of any other cycle...
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74 @{$This->{IndependentCyclicPaths}} = ();
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75
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76 return $This;
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77 }
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78
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79 # Initialize class ...
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80 sub _InitializeClass {
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81 #Class name...
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82 $ClassName = __PACKAGE__;
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83 }
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84
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85 # Detect all cycles in graph...
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86 #
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87 sub DetectCycles {
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88 my($This) = @_;
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89
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90 return $This->DetectCyclesUsingCollapsingPathGraphMethodology();
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91 }
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92
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93 # Detect all cycles in the graph using collapsing path graph [Ref 31] methodology...
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94 #
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95 # Note:
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96 # . For topologically complex graphs containing large number of cycles,
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97 # CollapseVertexAndCollectCyclicPathsDetectCycles method implemented in
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98 # PathGraph can time out in which case no cycles are detected or
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99 # assigned.
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100 #
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101 sub DetectCyclesUsingCollapsingPathGraphMethodology {
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102 my($This) = @_;
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103 my($PathGraph);
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104
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105 # Create a path graph...
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106 $PathGraph = new Graph::PathGraph($This->{Graph});
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107
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108 # For a vertex to be in a cycle, its degree must be >=2. So delete vertices recursively
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109 # till all vertices with degree less than 2 have been deleted...
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110 $PathGraph->DeleteVerticesWithDegreeLessThan(2);
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111
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112 # Setup a VertexID and EdgeID to index map usage during retrieval of independent cycles to
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113 # avoid going over all vertices in all cylic paths later...
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114 #
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115 my($VertexIDsToIndicesRef, $LargestVertexIndex, $EdgeIDsToIndicesRef, $LargestEdgeIDIndex);
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116 ($VertexIDsToIndicesRef, $LargestVertexIndex) = $This->_SetupVertexIDsToIndicesMap($PathGraph);
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117 ($EdgeIDsToIndicesRef, $LargestEdgeIDIndex) = $This->_SetupEdgeIDsToIndicesMap($PathGraph);
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118
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119 # Recursively collapse vertices with lowest degree...
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120 my($VertexID, $CycleVertexID);
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121 while ($VertexID = $PathGraph->GetVertexWithSmallestDegree()) {
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122 if (!$PathGraph->CollapseVertexAndCollectCyclicPaths($VertexID)) {
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123 # Cycles detection didn't finish...
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124 return undef;
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125 }
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126 }
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127
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128 # Get detected cycles and save 'em sorted by size...
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129 push @{$This->{AllCyclicPaths}}, sort { $a->GetLength() <=> $b->GetLength() } $PathGraph->GetCyclicPaths();
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130
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131 # Retrieve independent cyclic paths...
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132 return $This->_RetrieveIndependentCycles($VertexIDsToIndicesRef, $LargestVertexIndex, $EdgeIDsToIndicesRef, $LargestEdgeIDIndex);
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133 }
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134
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135 # Retrieve and save independent cyclic paths...
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136 #
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137 # Set of independent cycles identified using this method doesn't correspond to basis set of
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138 # rings or smallest set of smallest rings (SSSR) [ Refs 29-30 ]; instead, set of cycles identified
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139 # as independent cycles simply correspond to cycles which contain no other cycle as their
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140 # subcycles and can't be described as linear combination of smaller cycles. And it also happen
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141 # to contain all the rings in basis set of rings and SSSR. In other words, it's a superset of basis set
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142 # of cycles and SSSR. For example, six four membered cycles are identified for cubane which is one
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143 # more than the basis set of cycles.
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144 #
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145 sub _RetrieveIndependentCycles {
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146 my($This, $VertexIDsToIndicesRef, $LargestVertexIndex, $EdgeIDsToIndicesRef, $LargestEdgeIDIndex) = @_;
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147
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148 # Only 1 or 0 cyclic paths...
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149 if (@{$This->{AllCyclicPaths}} <= 1) {
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150 push @{$This->{IndependentCyclicPaths}}, @{$This->{AllCyclicPaths}};
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151 return $This;
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152 }
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153
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154 # Setup bit vectors for each cyclic path with size of each bit vector corresponding to
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155 # maximum vertex index plus one...
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156 my($CyclicPath, $BitVector, @BitNums, @CyclicPathBitVectors, @CyclicPathEdgeIDsBitVectors);
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157
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158 @CyclicPathBitVectors = (); @CyclicPathEdgeIDsBitVectors = ();
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159
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160 # Set bits corresponding to VertexIDs EdgeIDs using their indices...
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161 for $CyclicPath (@{$This->{AllCyclicPaths}}) {
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162 $BitVector = new BitVector($LargestVertexIndex);
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163 @BitNums = map { $VertexIDsToIndicesRef->{$_} } $CyclicPath->GetVertices();
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164 $BitVector->SetBits(@BitNums);
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165 push @CyclicPathBitVectors, $BitVector;
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166
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167 $BitVector = new BitVector($LargestEdgeIDIndex);
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168 @BitNums = map { $EdgeIDsToIndicesRef->{$_} } $This->_GetPathEdgeIDs($CyclicPath);
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169 $BitVector->SetBits(@BitNums);
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170 push @CyclicPathEdgeIDsBitVectors, $BitVector;
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171 }
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172
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173 # First smallest cyclic path always ends up as an independent cyclic path...
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174 push @{$This->{IndependentCyclicPaths}}, $This->{AllCyclicPaths}[0];
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175
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176 # Retrieve other independent cyclic paths...
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177 my($CurrentIndex, $PreviousIndex, $CurrentCyclicPath, $PreviousCyclicPath, $CurrentPathLength, $PreviousPathLength, $CurrentBitVector, $PreviousBitVector, $CurrentAndPreviousBitVectpor, $AllPreviousSmallerPathsBitVector, $AllPreviousSmallerPathsEdgeIDsBitVector, $CurrentEdgeIDsBitVector, $AndBitVector, %SmallerPathAlreadyAdded, %SkipPath);
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178
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179 %SkipPath = ();
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180 %SmallerPathAlreadyAdded = ();
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181 $AllPreviousSmallerPathsBitVector = new BitVector($LargestVertexIndex);
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182 $AllPreviousSmallerPathsEdgeIDsBitVector = new BitVector($LargestEdgeIDIndex);
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183
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184 CURRENT: for $CurrentIndex (1 .. $#{$This->{AllCyclicPaths}}) {
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185 if (exists $SkipPath{$CurrentIndex}) {
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186 next CURRENT;
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187 }
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188 $CurrentCyclicPath = $This->{AllCyclicPaths}[$CurrentIndex];
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189 $CurrentBitVector = $CyclicPathBitVectors[$CurrentIndex];
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190 $CurrentPathLength = $CurrentCyclicPath->GetLength();
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191
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192 PREVIOUS: for $PreviousIndex (0 .. ($CurrentIndex - 1)) {
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193 if (exists $SkipPath{$PreviousIndex}) {
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194 next PREVIOUS;
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195 }
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196 $PreviousCyclicPath = $This->{AllCyclicPaths}[$PreviousIndex];
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197 $PreviousBitVector = $CyclicPathBitVectors[$PreviousIndex];
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198
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199 # Is previous path a subset of current path?
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200 $CurrentAndPreviousBitVectpor = $PreviousBitVector & $CurrentBitVector;
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201 if ($PreviousBitVector->GetNumOfSetBits() == $CurrentAndPreviousBitVectpor->GetNumOfSetBits()) {
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202 # Current path doesn't qualify an independent path...
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203 $SkipPath{$CurrentIndex} = 1;
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204 next CURRENT;
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205 }
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206
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207 $PreviousPathLength = $PreviousCyclicPath->GetLength();
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208 if ($PreviousPathLength < $CurrentPathLength) {
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209 # Mark cycle vertices seen in cyclic paths with length smaller than current path...
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210 if (! exists $SmallerPathAlreadyAdded{$PreviousIndex}) {
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211 $SmallerPathAlreadyAdded{$PreviousIndex} = 1;
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212 $AllPreviousSmallerPathsBitVector = $AllPreviousSmallerPathsBitVector | $PreviousBitVector;
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213 $AllPreviousSmallerPathsEdgeIDsBitVector = $AllPreviousSmallerPathsEdgeIDsBitVector | $CyclicPathEdgeIDsBitVectors[$PreviousIndex];
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214 }
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215 }
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216 }
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217 if ($AllPreviousSmallerPathsBitVector->GetNumOfSetBits()) {
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218 # Is current path a linear combination of smaller paths?
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219 $AndBitVector = $AllPreviousSmallerPathsBitVector & $CurrentBitVector;
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220 if ($CurrentBitVector->GetNumOfSetBits() == $AndBitVector->GetNumOfSetBits()) {
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221 # Are all edges in the current path already present in smaller paths?
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222 $CurrentEdgeIDsBitVector = $CyclicPathEdgeIDsBitVectors[$CurrentIndex];
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223 $AndBitVector = $AllPreviousSmallerPathsEdgeIDsBitVector & $CurrentEdgeIDsBitVector;
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224
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225 if ($CurrentEdgeIDsBitVector->GetNumOfSetBits() == $AndBitVector->GetNumOfSetBits()) {
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226 # Current path doesn't qualify an independent path...
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227 $SkipPath{$CurrentIndex} = 1;
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228 next CURRENT;
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229 }
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230 }
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231 }
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232 # It's an independent cyclic path...
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233 push @{$This->{IndependentCyclicPaths}}, $CurrentCyclicPath;
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234 }
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235 return $This;
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236 }
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237
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238 # Setup a VertexID to index map...
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239 #
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240 sub _SetupVertexIDsToIndicesMap {
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241 my($This, $PathGraph) = @_;
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242 my($LargestVertexIndex, @VertexIDs, %VertexIDsMap);
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243
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244 %VertexIDsMap = (); @VertexIDs = (); $LargestVertexIndex = 0;
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245
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246 @VertexIDs = $PathGraph->GetVertices();
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247 if (! @VertexIDs) {
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248 return (\%VertexIDsMap, $LargestVertexIndex);
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249 }
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250 @VertexIDsMap{ @VertexIDs } = (0 .. $#VertexIDs);
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251 $LargestVertexIndex = scalar @VertexIDs;
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252
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253 return (\%VertexIDsMap, $LargestVertexIndex);
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254 }
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255
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256 # Setup a Edge to index map using paths associated to egdes in an intial
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257 # path graph...
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258 #
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259 sub _SetupEdgeIDsToIndicesMap {
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260 my($This, $PathGraph) = @_;
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261 my($Path, $LargestEdgeIndex, @EdgeIDs, %EdgeIDsMap);
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262
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263 %EdgeIDsMap = (); @EdgeIDs = (); $LargestEdgeIndex = 0;
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264
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265 @EdgeIDs = ();
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266 for $Path ($PathGraph->GetPaths()) {
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267 push @EdgeIDs, $This->_GetPathEdgeIDs($Path);
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268 }
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269
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270 if (! @EdgeIDs) {
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271 return (\%EdgeIDsMap, $LargestEdgeIndex);
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272 }
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273
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274 @EdgeIDsMap{ @EdgeIDs } = (0 .. $#EdgeIDs);
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275 $LargestEdgeIndex = scalar @EdgeIDs;
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276
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277 return (\%EdgeIDsMap, $LargestEdgeIndex);
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278 }
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279
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280 # Get path edge IDs or number of edges. The edge IDs are generated from
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281 # edge vertices and correpond to VertexID1-VertexID2 where VertexID1 <=
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282 # VertexID2.
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283 #
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284 sub _GetPathEdgeIDs {
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285 my($This, $Path) = @_;
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286 my(@EdgesVertexIDs, @EdgeIDs);
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287
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288 @EdgesVertexIDs = (); @EdgeIDs = ();
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289 @EdgesVertexIDs = $Path->GetEdges();
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290 if (!@EdgesVertexIDs) {
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291 return wantarray ? @EdgeIDs : (scalar @EdgeIDs);
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292 }
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293
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294 # Set up edge IDs...
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295 my($Index, $VertexID1, $VertexID2, $EdgeID);
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296
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297 for ($Index = 0; $Index < $#EdgesVertexIDs; $Index += 2) {
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298 $VertexID1 = $EdgesVertexIDs[$Index]; $VertexID2 = $EdgesVertexIDs[$Index + 1];
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299 $EdgeID = ($VertexID1 <= $VertexID2) ? "$VertexID1-$VertexID2" : "$VertexID2-$VertexID1";
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300 push @EdgeIDs, $EdgeID;
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301 }
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302
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303 return wantarray ? @EdgeIDs : (scalar @EdgeIDs);
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304 }
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305
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306 # Return an array containing references to cyclic paths or number of cylic paths...
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307 #
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308 sub GetAllCyclicPaths {
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309 my($This) = @_;
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310
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311 return wantarray ? @{$This->{AllCyclicPaths}} : scalar @{$This->{AllCyclicPaths}};
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312 }
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313
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314 # Get cyclic paths which are independent. In otherwords, cycles which don't contain any other
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315 # cycle as their subset...
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316 #
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317 sub GetIndependentCyclicPaths {
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318 my($This) = @_;
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319
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320 return wantarray ? @{$This->{IndependentCyclicPaths}} : scalar @{$This->{IndependentCyclicPaths}};
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321 }
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322
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323 # Return a string containg data for CyclesDetection object...
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324 sub StringifyCyclesDetection {
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325 my($This) = @_;
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326 my($CyclesDetectionString, $CyclesCount, $CyclicPath);
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327
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328 $CyclesCount = @{$This->{AllCyclicPaths}};
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329 $CyclesDetectionString = "AllCycles: Count - $CyclesCount";
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330 for $CyclicPath (@{$This->{AllCyclicPaths}}) {
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331 $CyclesDetectionString .= "; Cycle: " . join('-', $CyclicPath->GetVertices());
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332 }
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333
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334 $CyclesCount = @{$This->{IndependentCyclicPaths}};
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335 $CyclesDetectionString .= "\nIndependentCycles: Count - $CyclesCount";
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336 for $CyclicPath (@{$This->{IndependentCyclicPaths}}) {
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337 $CyclesDetectionString .= "; Cycle: " . join('-', $CyclicPath->GetVertices());
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338 }
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339
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340 return $CyclesDetectionString;
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341 }
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342
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343 # Return a reference to new cycle detection object...
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344 sub Copy {
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345 my($This) = @_;
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346 my($NewCyclesDetection);
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347
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348 $NewCyclesDetection = Storable::dclone($This);
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349
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350 return $NewCyclesDetection;
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351 }
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352
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353 1;
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354
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355 __END__
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356
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357 =head1 NAME
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358
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359 CyclesDetection
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360
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361 =head1 SYNOPSIS
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362
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363 use Graph::CyclesDetection;
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364
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365 use Graph::CyclesDetection qw(:all);
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366
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367 =head1 DESCRIPTION
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368
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369 B<CyclesDetection> class provides the following methods:
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370
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371 new, Copy, DetectCycles, DetectCyclesUsingCollapsingPathGraphMethodology,
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372 GetAllCyclicPaths, GetIndependentCyclicPaths, StringifyCyclesDetection
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373
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374 Cycles in a B<Graph> are detected using collapsing path graph [Ref 31]
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375 methodology.
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376
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377 =head2 METHODS
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378
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379 =over 4
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380
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381 =item B<new>
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382
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383 $NewCyclesDetection = new Graph::CyclesDetection($Graph);
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384
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385 Using specified I<Graph>, B<new> method creates a new B<CyclesDetection> object and returns
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386 newly created B<CyclesDetection> object.
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387
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388 =item B<Copy>
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389
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390 $NewCyclesDetection = $CyclesDetection->Copy();
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391
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392 Copies I<CyclesDetection> and its associated data using B<Storable::dclone> and returns a new
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393 B<CyclesDetection> object.
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394
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395 =item B<DetectCycles>
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396
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397 $CyclesDetection->DetectCycles();
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398
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399 Detects all cycles in a graph and returns I<CyclesDetection>.
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400
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401 =item B<DetectCyclesUsingCollapsingPathGraphMethodology>
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402
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403 $CyclesDetection->DetectCyclesUsingCollapsingPathGraphMethodology();
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404
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405 Detects all cycles in a graph using collapsing path graph [Ref 31] methodology
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406 and returns I<CyclesDetection>.
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407
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408 =item B<GetAllCyclicPaths>
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409
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410 @AllCyclicPaths = $CyclesDetection->GetAllCyclicPaths();
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411 $NumOfAllCyclicPaths = $CyclesDetection->GetAllCyclicPaths();
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412
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413 Returns an array containing references to all cyclic paths identified during cycles
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414 detection. In scalar text, number of cycles is returned.
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415
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416 =item B<GetIndependentCyclicPaths>
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417
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418 @IndependentCyclicPaths = $CyclesDetection->GetAllCyclicPaths();
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419 $NumOfIndependentCyclicPaths = $CyclesDetection->GetAllCyclicPaths();
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420
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421 Returns an array containing references to independent cyclic paths identified during cycles
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422 detection. In scalar text, number of cycles is returned.
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423
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424 A set of independent cycles identified during cycles detection doesn't correspond to the basis set of
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425 rings or smallest set of smallest rings (SSSR) [ Refs 29-30 ]; instead, set of cycles indentified
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426 as independent cycles simply correpond to cycles which contain no other cycle as their
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427 subcycles and can't be described as a linear combination of smaller cycles. And it also happens
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428 to contain all the rings in basis set of rings and SSSR. In other words, it's a superset of a basis set
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429 of cycles and SSSR. For example, six four membered cycles are indentified for cubane, which is one
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430 more than the basis set of cycles.
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431
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432 =item B<StringifyCyclesDetection>
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433
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434 $String = $CyclesDetection->StringifyCyclesDetection();
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435
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436 Returns a string containing information about I<CyclesDetection> object.
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437
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438 =back
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439
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440 =head1 AUTHOR
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441
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442 Manish Sud <msud@san.rr.com>
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443
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444 =head1 SEE ALSO
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445
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446 Graph.pm, Path.pm, PathGraph.pm
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447
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448 =head1 COPYRIGHT
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449
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450 Copyright (C) 2015 Manish Sud. All rights reserved.
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451
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452 This file is part of MayaChemTools.
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453
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454 MayaChemTools is free software; you can redistribute it and/or modify it under
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455 the terms of the GNU Lesser General Public License as published by the Free
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456 Software Foundation; either version 3 of the License, or (at your option)
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457 any later version.
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458
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459 =cut
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