LABELED SHORTEST PATHS IN DIGRAPHSWITH NEGATIVE AND POSITIVE EDGE WEIGHTS

This paper gives a shortest path algorithm for CFG (contextfree grammar) labeled and weighted digraphs where edge weightsmay be positive or negative, but negative-weight cycles are not allowedin the underlying unlabeled graph. These results build directly on analgorithm of Barrett et al. [SIAM J. Comput. 30 (2000) 809–837]. Inaddition to many other results, they gave a shortest path algorithm forCFG labeled and weighted digraphs where all edges are nonnegative.Our algorithm is based closely on Barrett et al.’s algorithm as well asJohnson’s algorithm for shortest paths in digraphs whose edges mayhave positive or negative weights