Labeled shortest paths in digraphs with negative and positive edge weights
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 3, pp. 567-583.

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.

DOI: 10.1051/ita/2009011
Classification: 68Q25,  52B05,  68Q42,  05C78
Keywords: shortest paths, negative and positive edge weights, context free grammars
@article{ITA_2009__43_3_567_0,
author = {Bradford, Phillip G. and Thomas, David A.},
title = {Labeled shortest paths in digraphs with negative and positive edge weights},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {567--583},
publisher = {EDP-Sciences},
volume = {43},
number = {3},
year = {2009},
doi = {10.1051/ita/2009011},
zbl = {1175.68196},
mrnumber = {2541131},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita/2009011/}
}
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 - Informatique Théorique et Applications
PY  - 2009
DA  - 2009///
SP  - 567
EP  - 583
VL  - 43
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita/2009011/
UR  - https://zbmath.org/?q=an%3A1175.68196
UR  - https://www.ams.org/mathscinet-getitem?mr=2541131
UR  - https://doi.org/10.1051/ita/2009011
DO  - 10.1051/ita/2009011
LA  - en
ID  - ITA_2009__43_3_567_0
ER  - 
%0 Journal Article
%A Bradford, Phillip G.
%A Thomas, David A.
%T Labeled shortest paths in digraphs with negative and positive edge weights
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2009
%P 567-583
%V 43
%N 3
%I EDP-Sciences
%U https://doi.org/10.1051/ita/2009011
%R 10.1051/ita/2009011
%G en
%F ITA_2009__43_3_567_0
Bradford, Phillip G.; Thomas, David A. Labeled shortest paths in digraphs with negative and positive edge weights. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 3, pp. 567-583. doi : 10.1051/ita/2009011. http://www.numdam.org/articles/10.1051/ita/2009011/

[1] C. Barrett, R. Jacob and M. Marathe, Formal-language-constrained path problems. SIAM J. Comput. 30 (2000) 809-837. | MR | Zbl

[2] 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

[3] 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. | Zbl

[4] P.G. Bradford and V. Choppella, Fast Dyck and semi-Dyck constrained shortest paths on DAGs (submitted).

[5] D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions. J. Symb. Comput. 9 (1990) 251-280. | MR | Zbl

[6] T.H. Cormen, C.E. Leiserson, R.L. Rivest and C. Stein, Introduction to Algorithms, 2nd edition. MIT Press (2001). | MR | Zbl

[7] R. Greenlaw, H.J. Hoover and W.L. Ruzzo, Limits to Parallel Computation: P-Completeness Theory. Oxford University Press (1995). | MR | Zbl

[8] J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979). | MR | Zbl

[9] D.B. Johnson, Efficient algorithms for shortest paths in sparse networks. J. ACM 24(1) (1977) 1-13. | MR | Zbl

[10] A.O. Mendelzon and P.T. Wood, Finding regular simple paths in graph databases. SIAM J. Comput. 24 (1995) 1235-1258. | MR | Zbl

[11] M. Nykänen and E. Ukkonen, The exact path length problem. J. Algor. 42 (2002) 41-53. | MR | Zbl

[12] W.L. Ruzzo, Complete pushdown languages. Unpublished manuscript (1979).

[13] 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.

[14] U. Zwick, Exact and Approximate Distances in Graphs - A survey. In Proceedings of the Ninth ESA (2001) 33-48. | MR | Zbl

Cited by Sources: