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Issue RAIRO-Theor. Inf. Appl.
Volume 43, Number 3, July-September 2009
Page(s) 567 - 583
DOI 10.1051/ita/2009011
Published online 04 April 2009

RAIRO-Theor. Inf. Appl. 43, 567-583 (2009)
DOI: 10.1051/ita/2009011

Labeled shortest paths in digraphs with negative and positive edge weights

Phillip G. Bradford1 and David A. Thomas2

1  Department of Computer Science, The University of Alabama, Box 870290, Tuscaloosa, AL 35487-0290, USA; pgb@cs.ua.edu
2  Mercer University, Department of Computer Science, 1400 Coleman Ave, Macon, GA 31207, USA; David.A.Thomas@student.Mercer.edu


Received October 5, 2006. Accepted January 6, 2009. Published online 4 April 2009

Abstract
This paper gives a shortest path algorithm for CFG (context free grammar) labeled and weighted digraphs where edge weights may be positive or negative, but negative-weight cycles are not allowed in the underlying unlabeled graph. These results build directly on an algorithm of Barrett et al. [SIAM J. Comput. 30 (2000) 809–837]. In addition to many other results, they gave a shortest path algorithm for CFG labeled and weighted digraphs where all edges are nonnegative. Our algorithm is based closely on Barrett et al.'s algorithm as well as Johnson's algorithm for shortest paths in digraphs whose edges may have positive or negative weights.


Mathematics Subject Classification. 68Q25, 52B05, 68Q42, 05C78.

Key words: Shortest paths -- negative and positive edge weights -- context free grammars.


© EDP Sciences 2009


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