/usr/include/polymake/graph/all_spanningtrees.h is in libpolymake-dev-common 3.2r2-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 | /* Copyright (c) 1997-2018
Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
http://www.polymake.org
This program is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option) any
later version: http://www.gnu.org/licenses/gpl.txt.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
--------------------------------------------------------------------------------
*/
#ifndef POLYMAKE_GRAPH_ALL_SPANNINGTREES_H
#define POLYMAKE_GRAPH_ALL_SPANNINGTREES_H
#include "polymake/client.h"
#include "polymake/Array.h"
#include "polymake/Set.h"
#include "polymake/Graph.h"
#include "polymake/Bitset.h"
#include "polymake/graph/graph_iterators.h"
#include "polymake/graph/arc_linking.h"
/** @file all_spanningtrees.h
* Algorithm for generating all spanning trees of an undirected connected graph along the lines of.
* Donald E. Knuth,
* in:
* The Art of Computer Programming,
* Volume 4, Fascicle 4, 24-31, 2006, Pearson Education Inc.
*/
namespace polymake { namespace graph {
template <typename TGraph>
Set<int> initial_spanningtree(const TGraph& G)
{
Set<int> st;
BFSiterator<TGraph> BFS_spanningtree(G, 0);
Bitset visited;
do {
visited = BFS_spanningtree.node_visitor().get_visited_nodes();
int current = *BFS_spanningtree;
++BFS_spanningtree;
visited ^= BFS_spanningtree.node_visitor().get_visited_nodes();
for (auto it = visited.begin(); !it.at_end(); ++it) {
int i = 0;
for (auto eit = entire(edges(G)); !eit.at_end(); ++eit) {
if (eit.to_node() == std::min(current,*it) && eit.from_node() == std::max(current,*it) )
break;
else ++i;
}
st += i;
}
} while (!BFS_spanningtree.at_end());
return st;
}
Array<Set<int>> all_spanningtrees(const Graph<>& G)
{
typedef ArcLinking IM;
typedef ArcLinking::IncidenceCell IC;
typedef ArcLinking::ColumnObject CO;
std::list<Set<int>> st;
Array<IC*> arcs_by_id(G.edges());
IM ArcGraph(G, arcs_by_id);
//initialize variables for the algorithm
int n = G.nodes();
Array<IC*> a(n-1), s(n-2);
if (n-2 > 0)
s[0] = nullptr;
Array<int> b(n,-1);
Set<int> init_st = initial_spanningtree<>(G);
int st_index = 0;
for (auto it = entire(init_st); !it.at_end(); ++it, ++st_index) {
a[st_index] = arcs_by_id[*it];
}
int l = 0;
bool terminate = false, advancing = false, revert = false;
CO *u = 0, *v = 0;
IC *e = 0;
//execute the steps of the algorithm
while (!terminate) {
if (n>2) {
e = a[l+1];
u = ArcGraph.get_column_object(e->tip);
v = ArcGraph.get_column_object(ArcGraph.reverse(e)->tip);
if (u->size > v->size) {
std::swap(u,v);
e = ArcGraph.reverse(e);
}
e->link = ArcGraph.contract_edge(u,v);
a[l] = e;
++l;
if (l<n-2) {
s[l] = nullptr;
advancing = true;
}
else {
e = static_cast<IC*>(v->down);
advancing = false;
}
}
else {
v = ArcGraph.get_column_object(1);
e = static_cast<IC*>(ArcGraph.get_column_object(0)->down);
}
if (!advancing) {
Set<int> fixed_edges;
for (int j = 0; j < n-2; ++j) {
fixed_edges += a[j]->id;
}
Set<int> completing_edges = ArcGraph.ids_of_column(ArcGraph.get_column_object(ArcGraph.reverse(e)->tip));
for (auto it = entire(completing_edges); !it.at_end(); ++it) {
fixed_edges += *it;
st.push_back(fixed_edges);
fixed_edges -= *it;
}
a[n-2] = static_cast<IC*>(v->up);
revert = true;
}
while (revert && !terminate) {
--l;
if (l == -1)
terminate = true;
else {
e = a[l];
u = ArcGraph.get_column_object(e->tip);
v = ArcGraph.get_column_object(ArcGraph.reverse(e)->tip);
}
if (!terminate) {
ArcGraph.expand_edge(u,v,e->link);
bool bridge = true, exhausted = false;
int w = u->id;
b[w] = v->id;
while (bridge && !exhausted) {
auto cit = u->begin();
while (cit != u->end() && bridge) {
bool marked = false;
int z = (*cit)->tip;
if (b[z] != -1)
marked = true;
if (!marked && z != v->id) {
b[z] = v->id;
b[w] = z;
w = z;
marked = true;
}
if (!marked && static_cast<IC*>(*cit) != ArcGraph.reverse(e))
bridge = false;
if (bridge)
++cit;
}
if (bridge) {
u = ArcGraph.get_column_object(b[u->id]);
if (u == v) {
exhausted = true;
}
}
}
u = ArcGraph.get_column_object(e->tip);
while (u != v) {
w = b[u->id];
b[u->id] = -1;
u = ArcGraph.get_column_object(w);
}
if (bridge) {
e = s[l];
while (e != nullptr) {
u = ArcGraph.get_column_object(e->tip);
v = ArcGraph.get_column_object(ArcGraph.reverse(e)->tip);
ArcGraph.undelete_row(ArcGraph.reverse(e));
e = e->link;
}
}
else {
u = ArcGraph.get_column_object(e->tip);
e->link = s[l];
s[l] = e;
ArcGraph.delete_row(e);
revert = false;
}
}
}
}
Array< Set<int> > st_array(st);
return st_array;
}
} }
#endif // POLYMAKE_GRAPH_ALL_SPANNINGTREES_H
// Local Variables:
// c-basic-offset:3
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
|