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count.cc
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/* tinygraph -- exploring graph conjectures on small graphs
Copyright (C) 2015 Falk Hüffner
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 of the License, or
(at your option) any later version.
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.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
// Count the number of graphs on n nodes with a certain property.
#include "Classes.hh"
#include "EulerTransform.hh"
#include "Graph.hh"
#include "Invariants.hh"
#include "Subgraph.hh"
#include <ctime>
#include <map>
#include <functional>
auto maxCpuTime = 1e6;
using PropertyTest = std::function<bool(const Graph&)>;
struct Property {
Property(PropertyTest t, bool h, bool d)
: test(t), hereditary(h), determinedByConnectedComponents(d) { }
PropertyTest test;
// if G has the property, then also every induced subgraph of G has
bool hereditary;
// G has the property if and only if each connected subgraph has the property
bool determinedByConnectedComponents;
};
struct GengProperty {
GengProperty(int f, bool h, bool d)
: flag(f), hereditary(h), determinedByConnectedComponents(d) { }
int flag;
bool hereditary;
bool determinedByConnectedComponents;
};
std::map<std::string, Property> properties = {
{"3-colorable", {[](const Graph& g) { return Invariants::kColorable(g, 3); }, true, true}},
{"4-colorable", {[](const Graph& g) { return Invariants::kColorable(g, 4); }, true, true}},
{"5-colorable", {[](const Graph& g) { return Invariants::kColorable(g, 5); }, true, true}},
{"6-colorable", {[](const Graph& g) { return Invariants::kColorable(g, 6); }, true, true}},
{"7-colorable", {[](const Graph& g) { return Invariants::kColorable(g, 7); }, true, true}},
{"8-colorable", {[](const Graph& g) { return Invariants::kColorable(g, 8); }, true, true}},
{"9-colorable", {[](const Graph& g) { return Invariants::kColorable(g, 9); }, true, true}},
{"radius-2", {[](const Graph& g) { return Invariants::radius(g) == 2; }, false, false}},
{"diameter-2", {[](const Graph& g) { return Invariants::diameter(g) == 2; }, false, false}},
{"diameter-3", {[](const Graph& g) { return Invariants::diameter(g) == 3; }, false, false}},
{"diameter-4", {[](const Graph& g) { return Invariants::diameter(g) == 4; }, false, false}},
{"diameter-5", {[](const Graph& g) { return Invariants::diameter(g) == 5; }, false, false}},
{"diameter-6", {[](const Graph& g) { return Invariants::diameter(g) == 6; }, false, false}},
{"diameter-7", {[](const Graph& g) { return Invariants::diameter(g) == 7; }, false, false}},
{"diameter-8", {[](const Graph& g) { return Invariants::diameter(g) == 8; }, false, false}},
{"diameter-9", {[](const Graph& g) { return Invariants::diameter(g) == 9; }, false, false}},
{"diameter<=2", {[](const Graph& g) { return Invariants::diameter(g) <= 2; }, false, false}},
{"diameter<=3", {[](const Graph& g) { return Invariants::diameter(g) <= 3; }, false, false}},
{"diameter<=4", {[](const Graph& g) { return Invariants::diameter(g) <= 4; }, false, false}},
{"diameter<=5", {[](const Graph& g) { return Invariants::diameter(g) <= 5; }, false, false}},
{"diameter<=6", {[](const Graph& g) { return Invariants::diameter(g) <= 6; }, false, false}},
{"diameter<=7", {[](const Graph& g) { return Invariants::diameter(g) <= 7; }, false, false}},
{"diameter<=8", {[](const Graph& g) { return Invariants::diameter(g) <= 8; }, false, false}},
{"diameter<=9", {[](const Graph& g) { return Invariants::diameter(g) <= 9; }, false, false}},
{"P4-sparse", {Classes::isP4Sparse, true, true}},
{"bipartite", {Classes::isBipartite, true, true}},
{"chordal", {Classes::isChordal, true, true}},
{"cochordal",{[](const Graph& g) { return Classes::isChordal(g.complement()); },true, true}},
{"eulerian", {Classes::isEulerian, false, true}},
{"hamiltonian", {Classes::isHamiltonian, false, false}},
{"long-hole-free",{[](const Graph& g) { return !Subgraph::hasLongHole(g); }, true, true}},
{"monopolar", {Classes::isMonopolar, true, true}},
{"odd-hole-free", {[](const Graph& g) { return !Subgraph::hasOddHole(g); }, true, true}},
{"perfect", {Classes::isPerfect, true, true}},
{"well-covered", {Classes::isWellCovered, false, true}},
{"prime", {Classes::isPrime, false, false}},
{"split", {Classes::isSplit, true, false}},
{"split-cluster", {Classes::isSplitClusterGraph, true, false}},
{"threshold", {Classes::isThreshold, true, false}},
{"trivially-perfect", {Classes::isTriviallyPerfect, true, true}},
{"weakly-chordal",{Classes::isWeaklyChordal, true, true}},
{"weakly-perfect",{Classes::isWeaklyPerfect, false, false}},
{"distance-hereditary", {Classes::isDistanceHereditary, true, true}},
{"AT-free", {Classes::isATFree, true, true}},
{"elementary", {Classes::isElementary, true, true}},
{"Hoang", {Classes::isHoang, true, true}},
{"two-split", {Classes::isTwoSplit, true, false}},
{"planar", {Classes::isPlanar, true, true}},
{"cograph", {Classes::isCograph, true, true}},
{"asymmetric", {Classes::isAsymmetric, false, false}},
{"simplicial-free", {Classes::isSimplicialFree, false, true}},
{"two-edge-connected", {Classes::isTwoEdgeConnected, false, false}},
{"minimally-two-edge-connected", {Classes::isMinimallyTwoEdgeConnected, false, false}},
{"minimally-two-vertex-connected", {Classes::isMinimallyTwoVertexConnected, false, false}},
};
std::map<std::string, GengProperty> gengProperties = {
{"biconnected", {Graph::BICONNECTED, false, false}},
{"two-vertex-connected", {Graph::BICONNECTED, false, false}},
{"triangle-free", {Graph::TRIANGLE_FREE, true, true}},
{"induced-triangle-free", {Graph::TRIANGLE_FREE, true, true}},
{"square-free", {Graph::SQUARE_FREE, true, true}},
{"C4-free", {Graph::SQUARE_FREE, true, true}},
{"bipartite", {Graph::BIPARTITE, true, true}},
};
template<typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T>& v) {
for (size_t i = 0; i < v.size(); ++i) {
if (i)
out << ", ";
out << v[i];
}
return out;
}
bool startsWith(const std::string& s, const std::string& a) {
return s.compare(0, a.length(), a) == 0;
}
bool endsWith(const std::string& s, const std::string& e) {
if (s.length() < e.length())
return false;
return s.compare(s.length() - e.length(), e.length(), e) == 0;
}
int main(int argc, char* argv[]) {
bool hereditary = true;
bool connectedOnly = false;
PropertyTest propertyTest = 0;
std::string propertyName = "";
int gengFlags = 0;
int i = 1;
bool countLabeled = false;
if (i < argc && std::string(argv[i]) == "-l") {
countLabeled = true;
++i;
}
bool determinedByConnectedComponents = !countLabeled;
for (; i < argc; ++i) {
std::string type = argv[i];
PropertyTest test = 0;
if (type == "connected") {
connectedOnly = true;
gengFlags |= Graph::CONNECTED;
continue;
} else if (type == "tree") {
connectedOnly = true;
gengFlags |= Graph::TREE;
continue;
} else if (gengProperties.find(type) != gengProperties.end()) {
auto p = gengProperties.find(type)->second;
gengFlags |= p.flag;
hereditary &= p.hereditary;
determinedByConnectedComponents &= p.determinedByConnectedComponents;
if (propertyName != "")
propertyName += ' ';
propertyName += type;
continue;
} else if (properties.find(type) != properties.end()) {
auto p = properties.find(type)->second;
test = p.test;
hereditary &= p.hereditary;
determinedByConnectedComponents &= p.determinedByConnectedComponents;
if (propertyName != "")
propertyName += ' ';
propertyName += type;
} else if (endsWith(type, "-free")) {
if (propertyName != "")
propertyName += ' ';
type = type.substr(0, type.length() - std::string("-free").length());
bool induced = false;
if (startsWith(type, "induced-")) {
type = type.substr(std::string("induced-").length());
induced = true;
propertyName += "(induced) ";
} else {
propertyName += "(not necessarily induced) ";
}
Graph f = Graph::byName(type);
propertyName += f.name() + "-free";
test = std::not1(induced ? Subgraph::hasInducedTest(f) : Subgraph::hasTest(f));
determinedByConnectedComponents &= f.isConnected();
} else {
std::cerr << "unknown graph class\n";
exit(1);
}
if (!propertyTest)
propertyTest = test;
else
propertyTest = [propertyTest, test](const Graph& g) { return propertyTest(g) && test(g); };
}
if (determinedByConnectedComponents)
gengFlags |= Graph::CONNECTED;
bool doPrune = hereditary && propertyTest;
if (!propertyTest)
propertyTest = [](const Graph&) { return true; };
std::vector<bignum> counts;
std::vector<double> times;
for (int n = 0; n <= MAXN; ++n) {
auto tStart = double(std::clock()) / CLOCKS_PER_SEC;
std::cerr << "--- n = " << n;
if (times.size() >= 2) {
auto tn = times.back();
auto tn1 = times[times.size() - 2];
auto est = tn * (tn / tn1);
std::cerr << " estimated time: " << est << 's' << std::endl;
if (est > maxCpuTime)
return 0;
} else {
std::cerr << std::endl;
}
bignum count = 0;
auto counter = [&count,&propertyTest,&countLabeled](const Graph& g) {
if (propertyTest(g))
count += countLabeled ? g.numLabeledGraphs() : 1;
};
if (doPrune) {
Graph::enumerate(n, counter, std::not1(propertyTest), gengFlags);
} else {
Graph::enumerate(n, counter, gengFlags);
}
counts.push_back(count);
auto tEnd = double(std::clock()) / CLOCKS_PER_SEC;
double t = tEnd - tStart;
times.push_back(t);
std::cerr << "time: " << t << 's' << std::endl;
std::string un = countLabeled ? "" : "un";
if (connectedOnly && !determinedByConnectedComponents) {
std::cout << "number of connected " << propertyName
<< " undirected " << un << "labeled graph on n vertices:\n"
<< counts << std::endl;
if (!countLabeled)
std::cout << "number of connected non-" << propertyName
<< " undirected " << un << "labeled graph on n vertices:\n"
<< EulerTransform::connectedNonGraphs(counts) << std::endl;
} else if (!determinedByConnectedComponents) {
std::cout << "number of " << propertyName
<< " undirected " << un << "labeled graph on n vertices:\n"
<< counts << std::endl;
if (!countLabeled)
std::cout << "number of non-" << propertyName
<< " undirected " << un << "labeled graph on n vertices:\n"
<< EulerTransform::nonGraphs(counts) << std::endl;
} else {
auto countsGeneral = EulerTransform::transform(counts);
std::cout << "number of " << propertyName
<< " undirected " << un << "labeled graph on n vertices:\n"
<< countsGeneral << std::endl;
if (!countLabeled) {
std::cout << "number of non-" << propertyName
<< " undirected " << un << "labeled graph on n vertices:\n"
<< EulerTransform::nonGraphs(countsGeneral) << std::endl;
std::cout << "number of " << propertyName
<< " connected undirected " << un << "labeled graph on n vertices:\n"
<< counts << std::endl;
std::cout << "number of non-" << propertyName
<< " connected undirected " << un << "labeled graph on n vertices:\n"
<< EulerTransform::connectedNonGraphs(counts) << std::endl;
}
}
}
return 0;
}