permlib
0.2.6
Library for permutation computations
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00001 // --------------------------------------------------------------------------- 00002 // 00003 // This file is part of PermLib. 00004 // 00005 // Copyright (c) 2009-2011 Thomas Rehn <thomas@carmen76.de> 00006 // All rights reserved. 00007 // 00008 // Redistribution and use in source and binary forms, with or without 00009 // modification, are permitted provided that the following conditions 00010 // are met: 00011 // 1. Redistributions of source code must retain the above copyright 00012 // notice, this list of conditions and the following disclaimer. 00013 // 2. Redistributions in binary form must reproduce the above copyright 00014 // notice, this list of conditions and the following disclaimer in the 00015 // documentation and/or other materials provided with the distribution. 00016 // 3. The name of the author may not be used to endorse or promote products 00017 // derived from this software without specific prior written permission. 00018 // 00019 // THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 00020 // IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 00021 // OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 00022 // IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 00023 // INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 00024 // NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 00025 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 00026 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 00027 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 00028 // THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 00029 // 00030 // --------------------------------------------------------------------------- 00031 00032 00033 #ifndef RANDOMSCHREIERSIMSCONSTRUCTION_H_ 00034 #define RANDOMSCHREIERSIMSCONSTRUCTION_H_ 00035 00036 #include <permlib/construct/base_construction.h> 00037 #include <permlib/generator/random_generator.h> 00038 #include <permlib/bsgs.h> 00039 00040 #include <boost/cstdint.hpp> 00041 #include <boost/foreach.hpp> 00042 00043 namespace permlib { 00044 00046 00050 template <class PERM, class TRANS, typename Integer = boost::uint64_t> 00051 class RandomSchreierSimsConstruction : public BaseConstruction<PERM, TRANS> { 00052 public: 00054 00061 RandomSchreierSimsConstruction(unsigned int n, RandomGenerator<PERM> *rng, Integer knownOrder = 0, 00062 unsigned int minimalConsecutiveSiftingElementCount = 20, unsigned int maxIterationFactor = 10000); 00063 00065 00067 template <class ForwardIterator> 00068 BSGS<PERM, TRANS> construct(ForwardIterator generatorsBegin, ForwardIterator generatorsEnd, bool& guaranteedBSGS) const; 00069 00071 00081 template <class ForwardIterator, class InputIterator> 00082 BSGS<PERM, TRANS> construct(ForwardIterator generatorsBegin, ForwardIterator generatorsEnd, InputIterator prescribedBaseBegin, InputIterator prescribedBaseEnd, bool& guaranteedBSGS) const; 00083 00085 mutable unsigned int m_statRandomElementsConsidered; 00086 00088 const unsigned int m_minimalConsecutiveSiftingElementCount; 00089 00091 const unsigned int m_maxIterationFactor; 00092 private: 00093 RandomGenerator<PERM> *m_rng; 00094 Integer m_knownOrder; 00095 }; 00096 00097 // 00098 // ---- IMPLEMENTATION 00099 // 00100 00101 template <class PERM, class TRANS, typename Integer> 00102 RandomSchreierSimsConstruction<PERM,TRANS,Integer>::RandomSchreierSimsConstruction(unsigned int n, RandomGenerator<PERM> *rng, Integer knownOrder, 00103 unsigned int minimalConsecutiveSiftingElementCount, unsigned int maxIterationFactor) 00104 : BaseConstruction<PERM, TRANS>(n), m_statRandomElementsConsidered(0), m_minimalConsecutiveSiftingElementCount(minimalConsecutiveSiftingElementCount), 00105 m_maxIterationFactor(maxIterationFactor), m_rng(rng), m_knownOrder(knownOrder) 00106 { } 00107 00108 template <class PERM, class TRANS, typename Integer> 00109 template <class ForwardIterator> 00110 inline BSGS<PERM, TRANS> RandomSchreierSimsConstruction<PERM,TRANS,Integer>::construct(ForwardIterator generatorsBegin, ForwardIterator generatorsEnd, bool& guaranteedBSGS) const { 00111 return construct(generatorsBegin, generatorsEnd, BaseConstruction<PERM,TRANS>::empty, BaseConstruction<PERM,TRANS>::empty, guaranteedBSGS); 00112 } 00113 00114 template <class PERM, class TRANS, typename Integer> 00115 template <class ForwardIterator, class InputIterator> 00116 BSGS<PERM, TRANS> RandomSchreierSimsConstruction<PERM, TRANS, Integer> 00117 ::construct(ForwardIterator generatorsBegin, ForwardIterator generatorsEnd, InputIterator prescribedBaseBegin, InputIterator prescribedBaseEnd, bool& guaranteedBSGS) const 00118 { 00119 const unsigned int &n = this->m_n; 00120 BSGS<PERM, TRANS> ret(n); 00121 std::vector<dom_int> &B = ret.B; 00122 std::vector<TRANS> &U = ret.U; 00123 std::vector<std::list<typename PERM::ptr> > S; 00124 this->setup(generatorsBegin, generatorsEnd, prescribedBaseBegin, prescribedBaseEnd, ret, S); 00125 00126 unsigned int consecutiveSiftingElementCount = m_minimalConsecutiveSiftingElementCount; 00127 if (m_knownOrder > 0) { 00128 // remove consecutive sifting limit if we have the group order as Las Vegas-abort criterion 00129 consecutiveSiftingElementCount = m_maxIterationFactor; 00130 } 00131 const unsigned int maxIterationCount = B.size() * m_maxIterationFactor; 00132 for (unsigned int it = 0; it < maxIterationCount; ++it) { 00133 bool isProbableBSGS = true; 00134 for (unsigned int i = 0; i < consecutiveSiftingElementCount && ret.order() != m_knownOrder; ++i) { 00135 PERM g = m_rng->next(); 00136 ++m_statRandomElementsConsidered; 00137 PERM h(n); 00138 unsigned int j = ret.sift(g, h); 00139 if (j < B.size() || !h.isIdentity()) { 00140 // flush it, because we add it as a generator 00141 h.flush(); 00142 00143 if (j == B.size()) { 00144 dom_int gamma = n+1; 00145 if (ret.chooseBaseElement(h, gamma)) { 00146 B.push_back(gamma); 00147 } 00148 BOOST_ASSERT(j < B.size()); 00149 S.push_back(std::list<typename PERM::ptr>()); 00150 U.push_back(TRANS(n)); 00151 } 00152 00153 boost::shared_ptr<PERM> hPtr(new PERM(h)); 00154 S[j].insert(S[j].end(), hPtr); 00155 00156 ret.orbitUpdate(j, S[j], hPtr); 00157 isProbableBSGS = false; 00158 break; 00159 } 00160 } 00161 if (isProbableBSGS) 00162 break; 00163 } 00164 00165 this->mergeGenerators(S, ret); 00166 00167 // convenience check of group order 00168 guaranteedBSGS = ret.template order<Integer>() == m_knownOrder; 00169 00170 return ret; 00171 } 00172 00173 } 00174 00175 #endif // -- RANDOMSCHREIERSIMSCONSTRUCTION_H_