# Labeled shortest paths in digraphs with negative and positive edge weights

Phillip G. Bradford; David A. Thomas

RAIRO - Theoretical Informatics and Applications (2009)

- Volume: 43, Issue: 3, page 567-583
- ISSN: 0988-3754

## Access Full Article

top## Abstract

top## How to cite

topBradford, Phillip G., and Thomas, David A.. "Labeled shortest paths in digraphs with negative and positive edge weights." RAIRO - Theoretical Informatics and Applications 43.3 (2009): 567-583. <http://eudml.org/doc/250562>.

@article{Bradford2009,

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.
},

author = {Bradford, Phillip G., Thomas, David A.},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Shortest paths; negative and positive edge weights; context free grammars.; shortest paths; context-free grammars},

language = {eng},

month = {4},

number = {3},

pages = {567-583},

publisher = {EDP Sciences},

title = {Labeled shortest paths in digraphs with negative and positive edge weights},

url = {http://eudml.org/doc/250562},

volume = {43},

year = {2009},

}

TY - JOUR

AU - Bradford, Phillip G.

AU - Thomas, David A.

TI - Labeled shortest paths in digraphs with negative and positive edge weights

JO - RAIRO - Theoretical Informatics and Applications

DA - 2009/4//

PB - EDP Sciences

VL - 43

IS - 3

SP - 567

EP - 583

AB -
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.

LA - eng

KW - Shortest paths; negative and positive edge weights; context free grammars.; shortest paths; context-free grammars

UR - http://eudml.org/doc/250562

ER -

## References

top- C. Barrett, R. Jacob and M. Marathe, Formal-language-constrained path problems. SIAM J. Comput.30 (2000) 809–837. Zbl0968.68066
- 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 Zbl1143.90316
- C. Barrett, K. Bisset, R. Jacob, G. Konejevod and M. Marathe, 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. Zbl1019.68801
- P.G. Bradford and V. Choppella, Fast Dyck and semi-Dyck constrained shortest paths on DAGs (submitted).
- D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions. J. Symb. Comput.9 (1990) 251–280. Zbl0702.65046
- T.H. Cormen, C.E. Leiserson, R.L. Rivest and C. Stein, Introduction to Algorithms, 2nd edition. MIT Press (2001). Zbl1047.68161
- R. Greenlaw, H.J. Hoover and W.L. Ruzzo, Limits to Parallel Computation: P-Completeness Theory. Oxford University Press (1995). Zbl0829.68068
- J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979). Zbl0426.68001
- D.B. Johnson, Efficient algorithms for shortest paths in sparse networks. J. ACM24(1) (1977) 1–13. Zbl0343.68028
- A.O. Mendelzon and P.T. Wood, Finding regular simple paths in graph databases. SIAM J. Comput.24 (1995) 1235–1258. Zbl0845.68033
- M. Nykänen and E. Ukkonen, The exact path length problem. J. Algor.42 (2002) 41–53. Zbl1057.90049
- 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. Zbl1006.68543

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.