TY - GEN

T1 - Improved algorithms for detecting negative cost cycles in undirected graphs

AU - Gu, Xiaofeng

AU - Madduri, Kamesh

AU - Subramani, K.

AU - Lai, Hong Jian

PY - 2009/11/9

Y1 - 2009/11/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70350625456&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350625456&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02270-8_7

DO - 10.1007/978-3-642-02270-8_7

M3 - Conference contribution

AN - SCOPUS:70350625456

SN - 3642022693

SN - 9783642022692

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 40

EP - 50

BT - Frontiers in Algorithmics - Third International Workshop, FAW 2009, Proceedings

T2 - 3rd International Frontiers of Algorithmics Workshop, FAW 2009

Y2 - 20 June 2009 through 23 June 2009

ER -