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
Y1 - 2009
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.
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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 -