Abstract
Let P G (s,t) denote a shortest path between two nodes s and t in an undirected graph G with nonnegative edge weights. A replacement path at a node u ∈ P G (s,t) = (s, ⋯ ,u,v, ⋯ ,t) is defined as a shortest path P G − e(u,t) from u to t which does not make use of (u,v). In this paper, we focus on the problem of finding an edge e = (u,v) ∈ P G (s,t) whose removal produces a replacement path at node u such that the ratio of the length of P G − e(u,t) to the length of P G (u,t) is maximum. We define such an edge as an anti-block vital edge (AVE for short), and show that this problem can be solved in O(mn) time, where n and m denote the number of nodes and edges in the graph, respectively. Some applications of the AVE for two special traffic networks are shown.
The authors would like to acknowledge the support of research grant No. 70525004, 70471035, 70121001 from the NSF and No.20060401003 from the PSF Of China.
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Su, B., Xu, Q., Xiao, P. (2007). Finding the Anti-block Vital Edge of a Shortest Path Between Two Nodes. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_4
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DOI: https://doi.org/10.1007/978-3-540-73556-4_4
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