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Labeled shortest paths in digraphs with negative and positive edge weights

Published online by Cambridge University Press:  04 April 2009

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

Keywords

Shortest pathsnegative and positive edge weightscontext free grammars.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 3 , July 2009 , pp. 567 - 583
Copyright
© EDP Sciences, 2009

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References

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