ntrShort.c File Reference

Symbolic shortest paths algorithms. More...

#include "ntr.h"
#include "cuddInt.h"

Include dependency graph for ntrShort.c:

Functions
int	Ntr_ShortestPaths (DdManager *dd, BnetNetwork *net, NtrOptions *option)
	Computes shortest paths in a state graph. More...
static DdNode *	ntrBellman (DdManager *dd, DdNode *D, DdNode *source, DdNode **x, DdNode **y, int vars, int pr)
	Bellman-Ford algorithm for single-source shortest paths. More...
static DdNode *	ntrWarshall (DdManager *dd, DdNode *D, DdNode **x, DdNode **y, int vars, int pr)
	Floyd-Warshall algorithm for all-pair shortest paths.
static DdNode *	ntrSquare (DdManager *dd, DdNode *D, DdNode **x, DdNode **y, DdNode **z, int vars, int pr, int st)
	Repeated squaring algorithm for all-pairs shortest paths. More...

Detailed Description

Symbolic shortest paths algorithms.

This file contains the functions that implement the symbolic version of several shortest path algorithms described in the JFM paper on ADDs.

Author

Fabio Somenzi, Iris Bahar

Copyright

Copyright (c) 1995-2015, Regents of the University of Colorado

All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

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Neither the name of the University of Colorado nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

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Function Documentation

Ntr_ShortestPaths()

int Ntr_ShortestPaths	(	DdManager *	dd,
		BnetNetwork *	net,
		NtrOptions *	option
	)

Computes shortest paths in a state graph.

Computes shortest paths in the state transition graph of a network. Three methods are availabe:

• Bellman-Ford algorithm for single-source shortest paths; the algorithm computes the distance (number of transitions) from the initial states to all states.
• Floyd-Warshall algorithm for all-pair shortest paths.
• Repeated squaring algorithm for all-pair shortest paths.

Returns

1 in case of success; 0 otherwise.

Side effects ADD variables are created in the manager.

ntrBellman()

static DdNode* ntrBellman ( DdManager *  dd, DdNode *  D, DdNode *  source, DdNode **  x, DdNode **  y, int  vars, int  pr  )

static

Bellman-Ford algorithm for single-source shortest paths.

Returns

the vector of the distances of all states from the initial states.

In case of multiple initial states the distance for each state is from the nearest initial state. Negative-weight cycles are detected, though only in the naive way. (Lack of convergence after nodes-1 iterations.) In such a case, a constant ADD with value minus infinity is returned. Bellman-Ford is based on matrix-vector multiplication. The matrix is the distance matrix D(x,y), such that D(a,b) is the length of the arc connecting state a to state b. The vector V(x) stores the distances of all states from the initial states. The actual vector used in the matrix-vector multiplication is diff(x), that holds those distances that have changed during the last update.

See also

ntrWarshall ntrSquare

ntrSquare()

static DdNode* ntrSquare ( DdManager *  dd, DdNode *  D, DdNode **  x, DdNode **  y, DdNode **  z, int  vars, int  pr, int  st  )

static

Repeated squaring algorithm for all-pairs shortest paths.

Parameters

dd	manager
D	D(z,y): distance matrix
x	array of x variables
y	array of y variables
z	array of z variables
vars	number of variables in each of the three arrays
pr	verbosity level
st	use the selective trace algorithm