/* Copyright (C) 2006-2008 Joris Mooij [joris dot mooij at tuebingen dot mpg dot de]
Radboud University Nijmegen, The Netherlands /
Max Planck Institute for Biological Cybernetics, Germany
This file is part of libDAI.
libDAI 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.
libDAI 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 libDAI; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*/
/// \file
/// \brief Defines BipartiteGraph class
#ifndef __defined_libdai_bipgraph_h
#define __defined_libdai_bipgraph_h
#include
#include
#include
#include
#include
namespace dai {
/// Represents the neighborhood structure of nodes in a bipartite graph.
/** A bipartite graph has two types of nodes: type 1 and type 2. Edges can occur only between
* nodes of different type. Nodes are indexed by an unsigned integer. If there are nr1()
* nodes of type 1 and nr2() nodes of type 2, the nodes of type 1 are numbered
* 0,1,2,...,nr1()-1 and the nodes of type 2 are numbered 0,1,2,...,nr2()-1. An edge
* between node \a n1 of type 1 and node \a n2 of type 2 is represented by a BipartiteGraph::Edge(\a n1,\a n2).
*
* A BipartiteGraph is implemented as a sparse adjacency list, i.e., it stores for each node a list of
* its neighboring nodes. In particular, it stores for each node of type 1 a vector of Neighbor structures
* (accessible by the nb1() method) describing the neighboring nodes of type 2; similarly, for each node
* of type 2 it stores a vector of Neighbor structures (accessibly by the nb2() method) describing the
* neighboring nodes of type 1.
* Thus, each node has an associated variable of type BipartiteGraph::Neighbors, which is a vector of
* Neighbor structures, describing its neighboring nodes of the other type.
* \idea Cache second-order neighborhoods in BipartiteGraph.
*/
class BipartiteGraph {
public:
/// Describes the neighbor relationship of two nodes in a BipartiteGraph.
/** Sometimes we want to do an action, such as sending a
* message, for all edges in a graph. However, most graphs
* will be sparse, so we need some way of storing a set of
* the neighbors of a node, which is both fast and
* memory-efficient. We also need to be able to go between
* viewing node \a A as a neighbor of node \a B, and node \a
* B as a neighbor of node \a A. The Neighbor struct solves
* both of these problems. Each node has a list of neighbors,
* stored as a vector, and extra information is
* included in the Neighbor struct which allows us to access
* a node as a neighbor of its neighbor (the \a dual member).
*
* By convention, variable identifiers naming indices into a
* vector of neighbors are prefixed with an underscore ("_").
* The neighbor list which they point into is then understood
* from context. For example:
*
* \code
* void BP::calcNewMessage( size_t i, size_t _I )
* \endcode
*
* Here, \a i is the "absolute" index of node i, but \a _I is
* understood as a "relative" index, giving node I's entry in
* nb1(i). The corresponding Neighbor structure can be
* accessed as nb1(i,_I) or nb1(i)[_I]. The absolute index of
* \a _I, which would be called \a I, can be recovered from
* the \a node member: nb1(i,_I).node. The \a iter member
* gives the relative index \a _I, and the \a dual member
* gives the "dual" relative index, i.e. the index of \a i in
* \a I's neighbor list.
*
* \code
* Neighbor n = nb1(i,_I);
* n.node == I &&
* n.iter == _I &&
* nb2(n.node,n.dual).node == i
* \endcode
*
* In a FactorGraph, nb1 is called nbV, and nb2 is called
* nbF.
*
* There is no easy way to transform a pair of absolute node
* indices \a i and \a I into a Neighbor structure relative
* to one of the nodes. Such a feature has never yet been
* found to be necessary. Iteration over edges can always be
* accomplished using the Neighbor lists, and by writing
* functions that accept relative indices:
* \code
* for( size_t i = 0; i < nrVars(); ++i )
* foreach( const Neighbor &I, nbV(i) )
* calcNewMessage( i, I.iter );
* \endcode
*/
struct Neighbor {
/// Corresponds to the index of this Neighbor entry in the vector of neighbors
size_t iter;
/// Contains the number of the neighboring node
size_t node;
/// Contains the "dual" iter
size_t dual;
/// Default constructor
Neighbor() {}
/// Constructor that sets the Neighbor members according to the parameters
Neighbor( size_t iter, size_t node, size_t dual ) : iter(iter), node(node), dual(dual) {}
/// Cast to size_t returns node member
operator size_t () const { return node; }
};
/// Describes the neighbors of some node.
typedef std::vector Neighbors;
/// Represents an edge: an Edge(\a n1,\a n2) corresponds to the edge between node \a n1 of type 1 and node \a n2 of type 2.
typedef std::pair Edge;
private:
/// Contains for each node of type 1 a vector of its neighbors
std::vector _nb1;
/// Contains for each node of type 2 a vector of its neighbors
std::vector _nb2;
/// Used internally by isTree()
struct levelType {
std::vector ind1; // indices of nodes of type 1
std::vector ind2; // indices of nodes of type 2
};
/// Support for some backwards compatibility with old interface
/** Call indexEdges() first to initialize these members
*/
bool _edge_indexed;
std::vector _edges;
hash_map _vv2e;
public:
/// Default constructor (creates an empty bipartite graph)
BipartiteGraph() : _nb1(), _nb2(), _edge_indexed(false) {}
/// Constructs BipartiteGraph from a range of edges.
/** \tparam EdgeInputIterator Iterator that iterates over instances of BipartiteGraph::Edge.
* \param nr1 The number of nodes of type 1.
* \param nr2 The number of nodes of type 2.
* \param begin Points to the first edge.
* \param end Points just beyond the last edge.
*/
template
BipartiteGraph( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end ) : _nb1( nr1 ), _nb2( nr2 ), _edge_indexed(false) {
construct( nr1, nr2, begin, end );
}
/// (Re)constructs BipartiteGraph from a range of edges.
/** \tparam EdgeInputIterator Iterator that iterates over instances of BipartiteGraph::Edge.
* \param nr1 The number of nodes of type 1.
* \param nr2 The number of nodes of type 2.
* \param begin Points to the first edge.
* \param end Points just beyond the last edge.
*/
template
void construct( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end );
/// Returns constant reference to the _i2'th neighbor of node i1 of type 1
const Neighbor & nb1( size_t i1, size_t _i2 ) const {
#ifdef DAI_DEBUG
assert( i1 < _nb1.size() );
assert( _i2 < _nb1[i1].size() );
#endif
return _nb1[i1][_i2];
}
/// Returns reference to the _i2'th neighbor of node i1 of type 1
Neighbor & nb1( size_t i1, size_t _i2 ) {
#ifdef DAI_DEBUG
assert( i1 < _nb1.size() );
assert( _i2 < _nb1[i1].size() );
#endif
return _nb1[i1][_i2];
}
/// Returns constant reference to the _i1'th neighbor of node i2 of type 2
const Neighbor & nb2( size_t i2, size_t _i1 ) const {
#ifdef DAI_DEBUG
assert( i2 < _nb2.size() );
assert( _i1 < _nb2[i2].size() );
#endif
return _nb2[i2][_i1];
}
/// Returns reference to the _i1'th neighbor of node i2 of type 2
Neighbor & nb2( size_t i2, size_t _i1 ) {
#ifdef DAI_DEBUG
assert( i2 < _nb2.size() );
assert( _i1 < _nb2[i2].size() );
#endif
return _nb2[i2][_i1];
}
/// Returns constant reference to all neighbors of node i1 of type 1
const Neighbors & nb1( size_t i1 ) const {
#ifdef DAI_DEBUG
assert( i1 < _nb1.size() );
#endif
return _nb1[i1];
}
/// Returns reference to all neighbors of node of i1 type 1
Neighbors & nb1( size_t i1 ) {
#ifdef DAI_DEBUG
assert( i1 < _nb1.size() );
#endif
return _nb1[i1];
}
/// Returns constant reference to all neighbors of node i2 of type 2
const Neighbors & nb2( size_t i2 ) const {
#ifdef DAI_DEBUG
assert( i2 < _nb2.size() );
#endif
return _nb2[i2];
}
/// Returns reference to all neighbors of node i2 of type 2
Neighbors & nb2( size_t i2 ) {
#ifdef DAI_DEBUG
assert( i2 < _nb2.size() );
#endif
return _nb2[i2];
}
/// Returns number of nodes of type 1
size_t nr1() const { return _nb1.size(); }
/// Returns number of nodes of type 2
size_t nr2() const { return _nb2.size(); }
/// Calculates the number of edges, time complexity: O(nr1())
size_t nrEdges() const {
size_t sum = 0;
for( size_t i1 = 0; i1 < nr1(); i1++ )
sum += nb1(i1).size();
return sum;
}
/// Adds a node of type 1 without neighbors.
void add1() { _nb1.push_back( Neighbors() ); }
/// Adds a node of type 2 without neighbors.
void add2() { _nb2.push_back( Neighbors() ); }
/// Adds a node of type 1, with neighbors specified by a range of nodes of type 2.
/** \tparam NodeInputIterator Iterator that iterates over instances of size_t.
* \param begin Points to the first index of the nodes of type 2 that should become neighbors of the added node.
* \param end Points just beyond the last index of the nodes of type 2 that should become neighbors of the added node.
* \param sizeHint For improved efficiency, the size of the range may be specified by sizeHint.
*/
template
void add1( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
Neighbors nbs1new;
nbs1new.reserve( sizeHint );
size_t iter = 0;
for( NodeInputIterator it = begin; it != end; ++it ) {
assert( *it < nr2() );
Neighbor nb1new( iter, *it, nb2(*it).size() );
Neighbor nb2new( nb2(*it).size(), nr1(), iter++ );
nbs1new.push_back( nb1new );
nb2( *it ).push_back( nb2new );
}
_nb1.push_back( nbs1new );
}
/// Adds a node of type 2, with neighbors specified by a range of nodes of type 1.
/** \tparam NodeInputIterator Iterator that iterates over instances of size_t.
* \param begin Points to the first index of the nodes of type 1 that should become neighbors of the added node.
* \param end Points just beyond the last index of the nodes of type 1 that should become neighbors of the added node.
* \param sizeHint For improved efficiency, the size of the range may be specified by sizeHint.
*/
template
void add2( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
Neighbors nbs2new;
nbs2new.reserve( sizeHint );
size_t iter = 0;
for( NodeInputIterator it = begin; it != end; ++it ) {
assert( *it < nr1() );
Neighbor nb2new( iter, *it, nb1(*it).size() );
Neighbor nb1new( nb1(*it).size(), nr2(), iter++ );
nbs2new.push_back( nb2new );
nb1( *it ).push_back( nb1new );
}
_nb2.push_back( nbs2new );
}
/// Removes node n1 of type 1 and all incident edges.
void erase1( size_t n1 );
/// Removes node n2 of type 2 and all incident edges.
void erase2( size_t n2 );
/// Adds an edge between node n1 of type 1 and node n2 of type 2.
/** If check == true, only adds the edge if it does not exist already.
*/
void addEdge( size_t n1, size_t n2, bool check = true ) {
assert( n1 < nr1() );
assert( n2 < nr2() );
bool exists = false;
if( check ) {
// Check whether the edge already exists
foreach( const Neighbor &nb2, nb1(n1) )
if( nb2 == n2 ) {
exists = true;
break;
}
}
if( !exists ) { // Add edge
Neighbor nb_1( _nb1[n1].size(), n2, _nb2[n2].size() );
Neighbor nb_2( nb_1.dual, n1, nb_1.iter );
_nb1[n1].push_back( nb_1 );
_nb2[n2].push_back( nb_2 );
}
}
/// Calculates second-order neighbors (i.e., neighbors of neighbors) of node n1 of type 1.
/** If include == true, includes n1 itself, otherwise excludes n1.
*/
std::vector delta1( size_t n1, bool include = false ) const;
/// Calculates second-order neighbors (i.e., neighbors of neighbors) of node n2 of type 2.
/** If include == true, includes n2 itself, otherwise excludes n2.
*/
std::vector delta2( size_t n2, bool include = false ) const;
/// Returns true if the graph is connected
/** \todo Should be optimized by invoking boost::graph library
*/
bool isConnected() const;
/// Returns true if the graph is a tree, i.e., if it is singly connected and connected.
bool isTree() const;
/// Writes this BipartiteGraph to an output stream in GraphViz .dot syntax
void printDot( std::ostream& os ) const;
// ----------------------------------------------------------------
// backwards compatibility layer
void indexEdges() {
_edges.clear();
_vv2e.clear();
size_t i=0;
foreach(const Neighbors &nb1s, _nb1) {
foreach(const Neighbor &n2, nb1s) {
Edge e(i, n2.node);
_edges.push_back(e);
}
i++;
}
sort(_edges.begin(), _edges.end()); // unnecessary?
i=0;
foreach(const Edge& e, _edges) {
_vv2e[e] = i++;
}
_edge_indexed = true;
}
const Edge& edge(size_t e) const {
assert(_edge_indexed);
return _edges[e];
}
const std::vector& edges() const {
return _edges;
}
size_t VV2E(size_t n1, size_t n2) const {
assert(_edge_indexed);
Edge e(n1,n2);
hash_map::const_iterator i = _vv2e.find(e);
assert(i != _vv2e.end());
return i->second;
}
size_t nr_edges() const {
assert(_edge_indexed);
return _edges.size();
}
private:
/// Checks internal consistency
void check() const;
};
template
void BipartiteGraph::construct( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end ) {
_nb1.clear();
_nb1.resize( nr1 );
_nb2.clear();
_nb2.resize( nr2 );
for( EdgeInputIterator e = begin; e != end; e++ ) {
#ifdef DAI_DEBUG
addEdge( e->first, e->second, true );
#else
addEdge( e->first, e->second, false );
#endif
}
}
} // end of namespace dai
/** \example example_bipgraph.cpp
* This example deals with the following bipartite graph:
* \dot
* graph example {
* ordering=out;
* subgraph cluster_type1 {
* node[shape=circle,width=0.4,fixedsize=true,style=filled];
* 12 [label="2"];
* 11 [label="1"];
* 10 [label="0"];
* }
* subgraph cluster_type2 {
* node[shape=polygon,regular=true,sides=4,width=0.4,fixedsize=true,style=filled];
* 21 [label="1"];
* 20 [label="0"];
* }
* 10 -- 20;
* 11 -- 20;
* 12 -- 20;
* 11 -- 21;
* 12 -- 21;
* }
* \enddot
* It has three nodes of type 1 (drawn as circles) and two nodes of type 2 (drawn as rectangles).
* Node 0 of type 1 has only one neighbor (node 0 of type 2), but node 0 of type 2 has three neighbors (nodes 0,1,2 of type 1).
* The example code shows how to construct a BipartiteGraph object representing this bipartite graph and
* how to iterate over nodes and their neighbors.
*
* \section Output
* \verbinclude examples/example_bipgraph.out
*
* \section Source
*/
#endif