Abstract
In this paper, we explore the design of algorithms for the problem of checking whether an undirected graph contains a negative cost cycle (UNCCD). It is known that this problem is significantly harder than the corresponding problem in directed graphs. Current approaches for solving this problem involve reducing it to either the b-matching problem or the T-join problem. The latter approach is more efficient in that it runs in O(n 3) time on a graph with n vertices and m edges, while the former runs in O(n 6) time. This paper shows that instances of the UNCCD problem, in which edge weights are restricted to be in the range { − K··K} can be solved in O(n 2.75·logn) time. Our algorithm is basically a variation of the T-join approach, which exploits the existence of extremely efficient shortest path algorithms in graphs with integral positive weights. We also provide an implementation profile of the algorithms discussed.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms and Applications. Prentice-Hall, Englewood Cliffs (1993)
Korte, B., Vygen, J.: Combinatorial Optimization. Algorithms and Combinatorics, vol. 21. Springer, New York (2000)
Gabow, H.N.: Data structures for weighted matching and nearest common ancestors with linking. In: Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery, pp. 434–443 (1990)
Shoshan, A., Zwick, U.: All pairs shortest paths in undirected graphs with integer weights. In: FOCS, pp. 605–615 (1999)
Gabow, H.N.: A scaling algorithm for weighted matching on general graphs. In: Proceedings 26th Annual Symposium of the Foundations of Computer Science, pp. 90–100. IEEE Computer Society Press, Los Alamitos (1985)
Demetrescu, C., Goldberg, A., Johnson, D.: 9th DIMACS implementation challenge – Shortest Paths (2005), http://www.dis.uniroma1.it/~challenge9/
Gabow, H.: Implementation of algorithms for maximum matching on non-bipartite graphs. PhD thesis, Stanford University (1974)
Rothberg, E.: Implementation of H. Gabow’s weighted matching algorithm (1992), ftp://dimacs.rutgers.edu/pub/netflow/matching/weighted/
Goldberg, A.V.: Scaling algorithms for the shortest paths problem. SIAM Journal on Computing 24, 494–504 (1995)
Goldberg, A.: Shortest path algorithms: Engineering aspects. In: ISAAC: 12th International Symposium on Algorithms and Computation, pp. 502–513 (2001)
Guo, L., Mukhopadhyay, S., Cukic, B.: Does your result checker really check? In: Dependable Systems and Networks, pp. 399–404 (2004)
Kratsch, D., McConnell, R.M., Mehlhorn, K., Spinrad, J.: Certifying algorithms for recognizing interval graphs and permutation graphs. In: SODA, pp. 158–167 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gu, X., Madduri, K., Subramani, K., Lai, HJ. (2009). Improved Algorithms for Detecting Negative Cost Cycles in Undirected Graphs. In: Deng, X., Hopcroft, J.E., Xue, J. (eds) Frontiers in Algorithmics. FAW 2009. Lecture Notes in Computer Science, vol 5598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02270-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-02270-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02269-2
Online ISBN: 978-3-642-02270-8
eBook Packages: Computer ScienceComputer Science (R0)