implement maximum cardinality search
* spot/twaalgos/mcs.cc, spot/twaalgos/mcs.hh: New files. * spot/twaalgos/Makefile.am: Add them. * python/spot/impl.i: Include mcs.hh. * bin/autfilt.cc: Add --mcs option. * NEWS: Mention it. * doc/spot.bib: Add reference. * tests/core/mcs.test: New file. * tests/Makefile.am: Add it.
This commit is contained in:
Alexandre Duret-Lutz
parent
77a17881a3
commit
7b0e15a7fb
9 changed files with 501 additions and 5 deletions
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@ -37,6 +37,7 @@ twaalgos_HEADERS = \
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compsusp.hh \
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contains.hh \
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copy.hh \
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couvreurnew.hh \
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cycles.hh \
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dbranch.hh \
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deadends.hh \
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@ -65,9 +66,9 @@ twaalgos_HEADERS = \
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magic.hh \
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mask.hh \
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matchstates.hh \
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mcs.hh \
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minimize.hh \
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mealy_machine.hh \
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couvreurnew.hh \
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neverclaim.hh \
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parity.hh \
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postproc.hh \
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@ -114,6 +115,7 @@ libtwaalgos_la_SOURCES = \
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complement.cc \
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compsusp.cc \
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contains.cc \
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couvreurnew.cc \
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cycles.cc \
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dbranch.cc \
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deadends.cc \
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@ -141,9 +143,9 @@ libtwaalgos_la_SOURCES = \
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magic.cc \
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mask.cc \
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matchstates.cc \
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mcs.cc \
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minimize.cc \
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mealy_machine.cc \
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couvreurnew.cc \
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ndfs_result.hxx \
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neverclaim.cc \
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parity.cc \
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196
spot/twaalgos/mcs.cc
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196
spot/twaalgos/mcs.cc
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@ -0,0 +1,196 @@
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// -*- coding: utf-8 -*-
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// Copyright (C) by the Spot authors, see the AUTHORS file for details.
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//
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// This file is part of Spot, a model checking library.
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//
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// Spot is free software; you can redistribute it and/or modify it
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// under the terms of the GNU General Public License as published by
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// the Free Software Foundation; either version 3 of the License, or
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// (at your option) any later version.
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//
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// Spot is distributed in the hope that it will be useful, but WITHOUT
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// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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// License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with this program. If not, see <http://www.gnu.org/licenses/>.
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#include "config.h"
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#include <spot/twa/twagraph.hh>
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#include <spot/twaalgos/mcs.hh>
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#include <spot/twaalgos/sccinfo.hh>
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namespace spot
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{
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namespace
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{
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struct mcs_vertex
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{
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// Each vertex is part of a circular doubly-linked list.
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mcs_vertex* prev = nullptr;
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mcs_vertex* next = nullptr;
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// The weight of a vertex, initially 0, is the number of
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// neighbors that already have an MCS-number. The weight is -1
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// if the vertex itself has an MCS-number.
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int weight = 0;
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};
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struct mcs_data
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{
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std::vector<mcs_vertex> vertex;
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// set is an array of doubly-linked list built using vertex elements
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std::vector<mcs_vertex*> set;
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// Initialy, all n vertices are in set[0]
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mcs_data(unsigned n)
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: vertex(n), set(n, nullptr)
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{
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// make a circular list of everything in vertex
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vertex[0].prev = &vertex[n - 1];
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for (unsigned i = 0; i < n - 1; i++)
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{
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vertex[i].next = &vertex[i + 1];
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vertex[i + 1].prev = &vertex[i];
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}
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vertex[n - 1].next = &vertex[0];
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set[0] = &vertex[0];
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}
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void remove_vertex(unsigned vertex_i, unsigned from_set)
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{
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mcs_vertex* v = &vertex[vertex_i];
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mcs_vertex* prev = v->prev;
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mcs_vertex* next = v->next;
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prev->next = next;
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next->prev = prev;
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if (v == set[from_set])
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set[from_set] = (v == next) ? nullptr : next;
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}
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void insert_vertex(unsigned vertex_i, unsigned to_set)
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{
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mcs_vertex* v = &vertex[vertex_i];
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mcs_vertex* next = set[to_set];
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if (next == nullptr)
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{
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v->prev = v;
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v->next = v;
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set[to_set] = v;
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}
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else
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{
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mcs_vertex* prev = next->prev;
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v->prev = prev;
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v->next = next;
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prev->next = v;
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next->prev = v;
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}
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}
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void increase_vertex_weight(unsigned vertex_i)
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{
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mcs_vertex* v = &vertex[vertex_i];
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if (v->weight >= 0)
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{
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remove_vertex(vertex_i, v->weight);
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++v->weight;
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insert_vertex(vertex_i, v->weight);
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}
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}
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unsigned select_any_vertex(unsigned from_set)
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{
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mcs_vertex* start = set[from_set];
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assert(start);
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return start - &vertex[0];
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}
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scc_info* si;
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unsigned select_best_vertex_scc(unsigned from_set)
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{
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mcs_vertex* start = set[from_set];
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assert(start);
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assert(si);
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unsigned best = start - &vertex[0];
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unsigned best_scc = si->scc_of(best);
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mcs_vertex* v = start->next;
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while (v != start)
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{
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unsigned i = v - &vertex[0];
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if (si->scc_of(i) > best_scc)
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{
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best = i;
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best_scc = si->scc_of(i);
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}
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v = v->next;
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}
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return best;
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}
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};
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}
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/// \brief Return an ordering of the vertices computed by
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/// a maximum cardinality search.
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///
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/// Unlike Tarjan's paper \cite tarjan.84.sicomp , where states are
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/// numbered from N to 1, this number the states from 0 to N-1,
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/// starting from the initial state. The next number is assigned to
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/// a state that maximizes the number of already-numbered neighbors.
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std::vector<unsigned>
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maximum_cardinality_search(const const_twa_graph_ptr& a, mcs_tie_break tie)
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{
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unsigned n = a->num_states();
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mcs_data data(n);
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// We need to compute the neighbors of each state independently of
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// the orientation of the edges.
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std::vector<std::set<unsigned>> neighbors(n);
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for (auto& e: a->edges())
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{
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neighbors[e.src].insert(e.dst);
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neighbors[e.dst].insert(e.src);
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}
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// How to break ties when selecting the next vertex?
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unsigned (mcs_data::* pick_state)(unsigned) = &mcs_data::select_any_vertex;
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if (tie == MCS_TIE_SCC)
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{
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data.si = new scc_info(a, scc_info_options::NONE);
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pick_state = &mcs_data::select_best_vertex_scc;
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}
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std::vector<unsigned> order(n, 0U); // order is α in Tarjan's paper
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unsigned index = 0; // index is n-i in Tarjan's paper
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int max_weight = 0; // max_weight is j in Tarjan's paper
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auto number_state = [&](unsigned i)
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{
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order[i] = index++;
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int& w = data.vertex[i].weight;
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data.remove_vertex(i, w);
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w = -1;
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for (unsigned j: neighbors[i])
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data.increase_vertex_weight(j);
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++max_weight;
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};
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unsigned init = a->get_init_state_number();
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number_state(init);
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while (index < n)
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{
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while (max_weight > 0 && data.set[max_weight] == nullptr)
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--max_weight;
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number_state((data.*pick_state)(max_weight));
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}
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return order;
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}
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twa_graph_ptr
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maximum_cardinality_search_reorder_here(twa_graph_ptr a, mcs_tie_break tie)
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{
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std::vector<unsigned> order = maximum_cardinality_search(a, tie);
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a->defrag_states(order, order.size());
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return a;
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}
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}
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63
spot/twaalgos/mcs.hh
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63
spot/twaalgos/mcs.hh
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@ -0,0 +1,63 @@
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// -*- coding: utf-8 -*-
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// Copyright (C) by the Spot authors, see the AUTHORS file for details.
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//
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// This file is part of Spot, a model checking library.
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//
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// Spot is free software; you can redistribute it and/or modify it
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// under the terms of the GNU General Public License as published by
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// the Free Software Foundation; either version 3 of the License, or
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// (at your option) any later version.
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//
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// Spot is distributed in the hope that it will be useful, but WITHOUT
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// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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// License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with this program. If not, see <http://www.gnu.org/licenses/>.
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#pragma once
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#include <spot/misc/common.hh>
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#include <spot/twa/fwd.hh>
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#include <vector>
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namespace spot
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{
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enum mcs_tie_break
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{
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///\brief Break ties by picking the first possible state.
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MCS_TIE_ANY = 0,
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/// \brief Break ties by picking states from the "highest" SCCs
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///
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/// This is based on the topological ordering of SCCs computed
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/// by scc_info. The initial state is always in the highest
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/// SCC, and the smallest SCC has no exit.
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MCS_TIE_SCC,
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};
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/// \brief Return an ordering of the vertices computed by
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/// a maximum cardinality search.
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///
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/// Unlike Tarjan's paper \cite tarjan.84.sicomp , where states are
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/// numbered from N to 1, this numbers the states from 0 to N-1,
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/// starting from the initial state. The next number is assigned to
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/// a state that maximizes the number of already-numbered neighbors.
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///
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/// This version returns a vector such that RESULTS[I] is the rank
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/// of state I in the computed order.
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///
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/// \param tie specify how to break ties.
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SPOT_API std::vector<unsigned>
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maximum_cardinality_search(const const_twa_graph_ptr& a,
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mcs_tie_break tie = MCS_TIE_ANY);
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/// \brief Reorder the state of \a a according to the order
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/// computed by maximum_cardinality_search().
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///
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/// This works in place and return the same automaton.
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SPOT_API twa_graph_ptr
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maximum_cardinality_search_reorder_here(twa_graph_ptr a,
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mcs_tie_break tie = MCS_TIE_ANY);
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}
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