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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

Barrett, C., Jacob, R. and Marathe, M., Formal-language-constrained path problems. SIAM J. Comput. 30 (2000) 809–837. CrossRef
C. Barrett, K. Bisset, M. Holzer, G. Konjevod, M. Marathe and D. Wagner, Label Constrained Shortest Path Algorithms: An Experimental Evaluation using Transportation Networks. Tech. Report: Virginia Tech (USA), Arizona State University (USA), and Karlsruhe University (Germany), Presented at at the workshop on the DIMACS Shortest-Path Challenge, http://i11www.ira.uka.de/algo/people/mholzer/publications/pdf/bbhkmw-lcspa-07.pdf
Barrett, C., Bisset, K., Jacob, R., Konejevod, G. and Marathe, M., Classical and contemporary shortest path problems in road networks: Implementation and experimental analysis of the TRANSMIS router. European Symposium on Algorithms (ESA 02). Lect. Notes Comput. Sci. 2461 (2002) 126–138. CrossRef
P.G. Bradford and V. Choppella, Fast Dyck and semi-Dyck constrained shortest paths on DAGs (submitted).
Coppersmith, D. and Winograd, S., Matrix multiplication via arithmetic progressions. J. Symb. Comput. 9 (1990) 251–280. CrossRef
T.H. Cormen, C.E. Leiserson, R.L. Rivest and C. Stein, Introduction to Algorithms, 2nd edition. MIT Press (2001).
R. Greenlaw, H.J. Hoover and W.L. Ruzzo, Limits to Parallel Computation: P-Completeness Theory. Oxford University Press (1995).
J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979).
D.B. Johnson, Efficient algorithms for shortest paths in sparse networks. J. ACM 24(1) (1977) 1–13.
Mendelzon, A.O. and Wood, P.T., Finding regular simple paths in graph databases. SIAM J. Comput. 24 (1995) 1235–1258. CrossRef
Nykänen, M. and Ukkonen, E., The exact path length problem. J. Algor. 42 (2002) 41–53. CrossRef
W.L. Ruzzo, Complete pushdown languages. Unpublished manuscript (1979).
M. Yannakakis, Graph-theoretic methods in database theory. In Proceedings of the Ninth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS '90). ACM, New York, NY (1990) 230–242.
U. Zwick, Exact and Approximate Distances in Graphs – A survey. In Proceedings of the Ninth ESA (2001) 33–48.