namespace dai {
-/// A BipartiteGraph represents a bipartite graph, with two types of nodes (both are numbered
-/// as 0,1,2,...), with edges only between nodes of different type. The edges are stored as
-/// lists of adjacent nodes for each node.
+/// A BipartiteGraph 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, edges are indexed as
+ * a pair of unsigned integers (where the pair (a,b) means the b'th neighbor of the a'th node).
+ * The BipartiteGraph stores neighborhood structures as vectors of vectors of Neighbor entries.
+ */
class BipartiteGraph {
public:
/// A Neighbor describes a neighboring node of some other node.
- /** Iterating over all neighbors of some node i can be done in the following way:
+ /** Iterating over all neighbors of node n1 of type 1 can be done in the following way:
* \code
- * foreach( const BipartiteGraph::Neighbor &I, nb1(i) ) {
- * size_t _I = I.iter;
- * size_t _i = I.dual;
- * // I == I.node;
- * // The _I'th neighbor of i is I, and the _i'th neighbor of I is i:
- * // nb1(i)[_I] == I, nb2(I)[_i] == i
+ * foreach( const BipartiteGraph::Neighbor &n2, nb1(n1) ) {
+ * size_t _n2 = n2.iter;
+ * size_t _n1 = n2.dual;
+ * // n2 == n2.node;
+ * // The _n2'th neighbor of n1 is n2, and the _n1'th neighbor of n2 is n1:
+ * // nb1(n1)[_n2] == n2, nb2(n2)[_n1] == n1
* }
* \endcode
*/
struct Neighbor {
- /// iter corresponds to the index of this Neighbor entry in the list of neighbors
+ /// Corresponds to the index of this Neighbor entry in the vector of neighbors
unsigned iter;
- /// node contains the number of the neighboring node
+ /// Contains the number of the neighboring node
unsigned node;
- /// dual contains the "dual" iter
+ /// Contains the "dual" iter
unsigned dual;
- /// cast to unsigned returns node
- operator unsigned () const { return node; };
+ /// Cast to unsigned returns node
+ operator unsigned () const { return node; }
+ /// Default constructor
+ Neighbor() {}
+ /// Constructor
+ Neighbor( size_t iter, size_t node, size_t dual ) : iter(iter), node(node), dual(dual) {}
};
- /// Neighbors is a vector of Neigbor entries
+ /// Neighbors is a vector of Neighbor entries; each node has an associated Neighbors variable, which describes its neighbors.
typedef std::vector<Neighbor> Neighbors;
- /// Edge is used as index of an edge
+ /// Edge is used as index of an edge: an Edge(a,b) corresponds to the edge between the a'th node and its b'th neighbor.
typedef std::pair<size_t,size_t> Edge;
private:
- /// _nb1 contains for each node of the first kind a list of its neighbors
+ /// _nb1 contains for each node of type 1 a vector of its neighbors
std::vector<Neighbors> _nb1;
- /// _nb2 contains for each node of the second kind a list of its neighbors
+ /// _nb2 contains for each node of type 2 a vector of its neighbors
std::vector<Neighbors> _nb2;
/// Used internally by isTree()
return *this;
}
- /// Create bipartite graph from a range of edges, encoded as pairs of node numbers
- /// (more precisely, a std::pair<unsigned, unsigned> where the first integer corresponds
- /// to the node of the first type, and the second integer corresponds to the node of the
- /// second type). nr1 is the number of nodes of the first type, nr2 the number of nodes
- /// of the second type. The values between the iterators begin and end should be of type Edge.
+ /// Create bipartite graph from a range of edges.
+ /** nr1 is the number of nodes of type 1, nr2 the number of nodes of type 2.
+ * The value_type of an EdgeInputIterator should be Edge.
+ */
template<typename EdgeInputIterator>
void create( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end );
- /// Construct bipartite graph from a range of edges, encoded as pairs of node numbers
- /// (more precisely, a std::pair<unsigned, unsigned> where the first integer corresponds
- /// to the node of the first type, and the second integer corresponds to the node of the
- /// second type). nr1 is the number of nodes of the first type, nr2 the number of nodes
- /// of the second type. The values between the iterators begin and end should be of type Edge.
+ /// Construct bipartite graph from a range of edges.
+ /** nr1 is the number of nodes of type 1, nr2 the number of nodes of type 2.
+ * The value_type of an EdgeInputIterator should be Edge.
+ */
template<typename EdgeInputIterator>
BipartiteGraph( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end ) : _nb1( nr1 ), _nb2( nr2 ) {
create( nr1, nr2, begin, end );
}
- /// Returns constant reference to the _i2'th neighbor of node i1 of first type
+ /// Returns constant reference to the _i2'th neighbor of node i1 of type 1
const Neighbor & nb1( size_t i1, size_t _i2 ) const { return _nb1[i1][_i2]; }
- /// Returns reference to the _i2'th neighbor of node i1 of first type
+ /// Returns reference to the _i2'th neighbor of node i1 of type 1
Neighbor & nb1( size_t i1, size_t _i2 ) { return _nb1[i1][_i2]; }
- /// Returns constant reference to the _i1'th neighbor of node i2 of second type
+ /// Returns constant reference to the _i1'th neighbor of node i2 of type 2
const Neighbor & nb2( size_t i2, size_t _i1 ) const { return _nb2[i2][_i1]; }
- /// Returns reference to the _i1'th neighbor of node i2 of second type
+ /// Returns reference to the _i1'th neighbor of node i2 of type 2
Neighbor & nb2( size_t i2, size_t _i1 ) { return _nb2[i2][_i1]; }
- /// Returns constant reference to all neighbors of node of first type
+ /// Returns constant reference to all neighbors of node i1 of type 1
const Neighbors & nb1( size_t i1 ) const { return _nb1[i1]; }
- /// Returns reference to all neighbors of node of first type
+ /// Returns reference to all neighbors of node of i1 type 1
Neighbors & nb1( size_t i1 ) { return _nb1[i1]; }
- /// Returns constant reference to all neighbors of node of second type
+ /// Returns constant reference to all neighbors of node i2 of type 2
const Neighbors & nb2( size_t i2 ) const { return _nb2[i2]; }
- /// Returns reference to all neighbors of node of second type
+ /// Returns reference to all neighbors of node i2 of type 2
Neighbors & nb2( size_t i2 ) { return _nb2[i2]; }
- /// Returns number of nodes of first type
+ /// Returns number of nodes of type 1
size_t nr1() const { return _nb1.size(); }
- /// Returns number of nodes of second type
+ /// Returns number of nodes of type 2
size_t nr2() const { return _nb2.size(); }
/// Calculates the number of edges
return sum;
}
- /// Add node of first type without neighbors.
+ /// Add node of type 1 without neighbors.
void add1() {
_nb1.push_back( Neighbors() );
}
- /// Add node of first type without neighbors.
+ /// Add node of type 2 without neighbors.
void add2() {
_nb2.push_back( Neighbors() );
}
- /// Add node of first type with neighbors specified by a range.
- /// For improved efficiency, the size of the range may be specified by sizeHint.
- /// *NodeInputIterator should be a size_t.
+ /// Add node of type 1 with neighbors specified by a range.
+ /** The value_type of an NodeInputIterator should be a size_t, corresponding to
+ * the indices of nodes of type 2 that should become neighbors of the added node.
+ * For improved efficiency, the size of the range may be specified by sizeHint.
+ */
template <typename NodeInputIterator>
void add1( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
Neighbors nbs1new;
size_t iter = 0;
for( NodeInputIterator it = begin; it != end; ++it ) {
assert( *it < nr2() );
-
- Neighbor nb1new;
- nb1new.node = *it;
- nb1new.iter = iter;
- nb1new.dual = nb2(*it).size();
-
- Neighbor nb2new;
- nb2new.node = nr1();
- nb2new.iter = nb2(*it).size();
- nb2new.dual = iter++;
-
+ 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 );
}
- /// Add node of second type with neighbors specified by a range.
- /// For improved efficiency, the size of the range may be specified by sizeHint.
- /// *NodeInputIterator should be a size_t.
+ /// Add node of type 2 with neighbors specified by a range.
+ /** The value_type of an NodeInputIterator should be a size_t, corresponding to
+ * the indices of nodes of type 1 that should become neighbors of the added node.
+ * For improved efficiency, the size of the range may be specified by sizeHint.
+ */
template <typename NodeInputIterator>
void add2( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
Neighbors nbs2new;
size_t iter = 0;
for( NodeInputIterator it = begin; it != end; ++it ) {
assert( *it < nr1() );
-
- Neighbor nb2new;
- nb2new.node = *it;
- nb2new.iter = iter;
- nb2new.dual = nb1(*it).size();
-
- Neighbor nb1new;
- nb1new.node = nr2();
- nb1new.iter = nb1(*it).size();
- nb1new.dual = iter++;
-
+ 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 );
}
- /// Remove node of first type
+ /// Remove node of type 1 and all incident edges.
void erase1( size_t n1 ) {
assert( n1 < nr1() );
// Erase neighbor entry of node n1
_nb1.erase( _nb1.begin() + n1 );
- // Adjust neighbor entries of nodes of second type
+ // Adjust neighbor entries of nodes of type 2
for( size_t n2 = 0; n2 < nr2(); n2++ )
for( size_t iter = 0; iter < nb2(n2).size(); ) {
if( nb2(n2, iter).node == n1 ) {
// delete this entry, because it points to the deleted node
nb2(n2).erase( nb2(n2).begin() + iter );
// adjust all subsequent entries:
- // update their iter and the corresponding dual of the neighboring node of the first kind
+ // update their iter and the corresponding dual of the neighboring node of type 1
for( size_t newiter = iter; newiter < nb2(n2).size(); newiter++ ) {
nb2( n2, newiter ).iter = newiter;
nb1( nb2(n2, newiter).node, nb2(n2, newiter).dual ).dual = newiter;
}
}
- /// Remove node of second type
+ /// Remove node of type 2 and all incident edges.
void erase2( size_t n2 ) {
assert( n2 < nr2() );
// Erase neighbor entry of node n2
_nb2.erase( _nb2.begin() + n2 );
- // Adjust neighbor entries of nodes of first type
+ // Adjust neighbor entries of nodes of type 1
for( size_t n1 = 0; n1 < nr1(); n1++ )
for( size_t iter = 0; iter < nb1(n1).size(); ) {
if( nb1(n1, iter).node == n2 ) {
// delete this entry, because it points to the deleted node
nb1(n1).erase( nb1(n1).begin() + iter );
// adjust all subsequent entries:
- // update their iter and the corresponding dual of the neighboring node of the first kind
+ // update their iter and the corresponding dual of the neighboring node of type 2
for( size_t newiter = iter; newiter < nb1(n1).size(); newiter++ ) {
nb1( n1, newiter ).iter = newiter;
nb2( nb1(n1, newiter).node, nb1(n1, newiter).dual ).dual = newiter;
}
}
- /// Calculate neighbors of neighbors of node n1 of first type.
- /// If include == true, include n1 itself, otherwise exclude n1.
+ /// Calculate second-order neighbors (i.e., neighbors of neighbors) of node n1 of type 1.
+ /** If include == true, include n1 itself, otherwise exclude n1.
+ */
std::vector<size_t> delta1( size_t n1, bool include = false ) const {
std::vector<size_t> result;
foreach( const Neighbor &n2, nb1(n1) )
return result;
}
- /// Calculate neighbors of neighbors of node n2 of second type
- /// If include == true, include n2 itself, otherwise exclude n2.
+ /// Calculate second-order neighbors (i.e., neighbors of neighbors) of node n2 of type 2.
+ /** If include == true, include n2 itself, otherwise exclude n2.
+ */
std::vector<size_t> delta2( size_t n2, bool include = false ) const {
std::vector<size_t> result;
foreach( const Neighbor &n1, nb2(n2) )
do {
found_new_nodes = false;
- // For all nodes of second type, check if they are connected with the (growing) component
+ // For all nodes of type 2, check if they are connected with the (growing) component
for( size_t n2 = 0; n2 < nr2(); n2++ )
if( !incomponent2[n2] ) {
foreach( const Neighbor &n1, nb2(n2) ) {
}
}
- // For all nodes of first type, check if they are connected with the (growing) component
+ // For all nodes of type 1, check if they are connected with the (growing) component
for( size_t n1 = 0; n1 < nr1(); n1++ )
if( !incomponent1[n1] ) {
foreach( const Neighbor &n2, nb1(n1) ) {
}
/// Returns true if the graph is a tree, i.e., if it is singly connected and connected.
- /// This is equivalent to whether for each pair of vertices in the graph, there exists
- /// a unique path in the graph that starts at the first and ends at the second vertex.
+ /** This is equivalent to whether for each pair of vertices in the graph, there exists
+ * a unique path in the graph that starts at the first and ends at the second vertex.
+ */
bool isTree() const {
using namespace std;
vector<levelType> levels;
}
if( foundCycle )
break;
- }
+ }
}
levels.push_back( newLevel );
nr_1 += newLevel.ind1.size();
for( EdgeInputIterator e = begin; e != end; e++ ) {
// Each edge yields a neighbor pair
- Neighbor nb_1;
- nb_1.iter = _nb1[e->first].size();
- nb_1.node = e->second;
- nb_1.dual = _nb2[e->second].size();
-
- Neighbor nb_2;
- nb_2.iter = nb_1.dual;
- nb_2.node = e->first;
- nb_2.dual = nb_1.iter;
-
+ Neighbor nb_1( _nb1[e->first].size(), e->second, _nb2[e->second].size() );
+ Neighbor nb_2( nb_1.dual, e->first, nb_1.iter );
_nb1[e->first].push_back( nb_1 );
_nb2[e->second].push_back( nb_2 );
}
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