Induced Subgraphs and Cliques

Provides functions dealing with induced subgraphs and finding cliques. More...

Classes
class	ogdf::CliqueFinderHeuristic
	Finds cliques and dense subgraphs using a heuristic. More...
class	ogdf::CliqueFinderModule
	Finds cliques. More...
class	ogdf::CliqueFinderSPQR
	Finds cliques using SPQR trees. More...

Functions
bool	ogdf::maximumDensitySubgraph (Graph &G, NodeSet< true > &subgraphNodes, std::function< node(node)> resultNodeMap=[](node v) { return v;}, int64_t timelimit=-1)
	Calculates the maximum density subgraph of G.

Methods for induced subgraphs
template<class LISTITERATOR >
void	ogdf::inducedSubGraph (const Graph &G, LISTITERATOR start, Graph &subGraph)
	Computes the subgraph induced by a list of nodes.
template<class LISTITERATOR >
void	ogdf::inducedSubGraph (const Graph &G, LISTITERATOR start, Graph &subGraph, NodeArray< node > &nodeTableOrig2New)
	Computes the subgraph induced by a list of nodes (plus a mapping from original nodes to new copies).
template<class LISTITERATOR >
void	ogdf::inducedSubGraph (const Graph &G, LISTITERATOR start, Graph &subGraph, NodeArray< node > &nodeTableOrig2New, EdgeArray< edge > &edgeTableOrig2New)
	Computes the subgraph induced by a list of nodes (plus mappings from original nodes and edges to new copies).
template<class LISTITERATOR >
void	ogdf::inducedSubGraph (const Graph &G, LISTITERATOR start, GraphCopySimple &subGraph)
	Computes the subgraph induced by a list of nodes.
template<class NODELISTITERATOR , class EDGELIST >
void	ogdf::inducedSubgraph (Graph &G, NODELISTITERATOR &it, EDGELIST &E)
	Computes the edges in a node-induced subgraph.

Detailed Description

Provides functions dealing with induced subgraphs and finding cliques.

Function Documentation

inducedSubGraph() [1/4]

template<class LISTITERATOR >

void ogdf::inducedSubGraph	(	const Graph &	G,
		LISTITERATOR	start,
		Graph &	subGraph
	)

Computes the subgraph induced by a list of nodes.

Template Parameters

LISTITERATOR

is the type of iterators for the input list of nodes.

Parameters

G	is the input graph.
start	is a list iterator pointing to the first element in a list of nodes, for which an induced subgraph shall be computed.
subGraph	is assigned the computed subgraph.

Definition at line 55 of file extended_graph_alg.h.

inducedSubGraph() [2/4]

template<class LISTITERATOR >

void ogdf::inducedSubGraph	(	const Graph &	G,
		LISTITERATOR	start,
		Graph &	subGraph,
		NodeArray< node > &	nodeTableOrig2New
	)

Computes the subgraph induced by a list of nodes (plus a mapping from original nodes to new copies).

Template Parameters

LISTITERATOR

is the type of iterators for the input list of nodes.

Parameters

G	is the input graph.
start	is a list iterator pointing to the first element in a list of nodes, for which an induced subgraph shall be computed.
subGraph	is assigned the computed subgraph.
nodeTableOrig2New	is assigned a mapping from the nodes in G to the nodes in subGraph.

Definition at line 72 of file extended_graph_alg.h.

inducedSubGraph() [3/4]

template<class LISTITERATOR >

void ogdf::inducedSubGraph	(	const Graph &	G,
		LISTITERATOR	start,
		Graph &	subGraph,
		NodeArray< node > &	nodeTableOrig2New,
		EdgeArray< edge > &	edgeTableOrig2New
	)

Computes the subgraph induced by a list of nodes (plus mappings from original nodes and edges to new copies).

Template Parameters

LISTITERATOR

is the type of iterators for the input list of nodes.

Parameters

G	is the input graph.
start	is a list iterator pointing to the first element in a list of nodes, for which an induced subgraph shall be computed.
subGraph	is assigned the computed subgraph.
nodeTableOrig2New	is assigned a mapping from the nodes in G to the nodes in subGraph.
edgeTableOrig2New	is assigned a mapping from the edges in G to the egdes in subGraph.

Definition at line 109 of file extended_graph_alg.h.

inducedSubGraph() [4/4]

template<class LISTITERATOR >

void ogdf::inducedSubGraph	(	const Graph &	G,
		LISTITERATOR	start,
		GraphCopySimple &	subGraph
	)

Computes the subgraph induced by a list of nodes.

Template Parameters

LISTITERATOR

is the type of iterators for the input list of nodes.

Parameters

G	is the input graph.
start	is a list iterator pointing to the first element in a list of nodes, for which an induced subgraph shall be computed.
subGraph	is assigned the computed subgraph, which will be set as a copy of G.

Definition at line 146 of file extended_graph_alg.h.

inducedSubgraph()

template<class NODELISTITERATOR , class EDGELIST >

void ogdf::inducedSubgraph	(	Graph &	G,
		NODELISTITERATOR &	it,
		EDGELIST &	E
	)

Computes the edges in a node-induced subgraph.

Template Parameters

NODELISTITERATOR	is the type of iterators for the input list of nodes.
EDGELIST	is the type of the returned edge list.

Parameters

G	is the input graph.
it	is a list iterator pointing to the first element in a list of nodes, whose induced subgraph is considered.
E	is assigned the list of edges in the node-induced subgraph.

Definition at line 179 of file extended_graph_alg.h.

maximumDensitySubgraph()

bool ogdf::maximumDensitySubgraph	(	Graph &	G,
		NodeSet< true > &	subgraphNodes,
		std::function< node(node)>	resultNodeMap = [](node v) { return v;},
		int64_t	timelimit = -1
	)

Calculates the maximum density subgraph of G.

Returns the subgraph of G given by the nodes of the subgraph. The subgraph with the highest density, which is \(\frac{|E|}{|V|}\) of the subgraph, is returned. The graph is treated as undirected and unweighted.

The algorithm is based on: A. V. Goldberg. Finding a maximum density subgraph. EECS Department, University of California, Berkeley. Technical Report No. UCB/CSD-84-171, 1984. https://www2.eecs.berkeley.edu/Pubs/TechRpts/1984/CSD-84-171.pdf

Internally, the MinSTCutMaxFlow algorithm (using MaxFlowGoldbergTarjan) is called \(\mathcal{O}(\log n)\) times. Assuming a runtime of \(\mathcal{O}(mn^2)\) for the min cut algorithm, the overall runtime is \(\mathcal{O}(mn^2\log n)\).

Side Effect

Note that the input graph G is modified. If this is not wanted, use a GraphCopy or GraphCopySimple.

resultNodeMap

resultNodeMap can be used if subgraphNodes does not belong to G. This helps when passing in a GraphCopy or GraphCopySimple:

NodeSet<true> subgraphNodes(G);
GraphCopySimple GC(G);
maximumDensitySubgraph(GC, subgraphNodes, [&](node n){ return GC.original(n);});

Parameters

G	is the input graph.
subgraphNodes	is the set of nodes inducing the subgraph.
resultNodeMap	maps each subgraph node (nodes of G) to some other node
timelimit	set to a value greater than -1 to set a timelimit in milliseconds. Note that 0 is a valid timelimit. When encountering a timelimit there is no valid result.

Returns

true, if the algorithm was successful and did not run into a timeout.