Finding the anti-block vital edge of a shortest path between two nodes

Authors:
Bing Su;Qingchuan Xu;Peng Xiao
Affiliations:
School of Management, Xi'an Jiaotong University, Xi'an, P.R. China and The State Key Lab for Manufacturing Systems Engineering, Xi'an, P.R. China;School of Management, Xi'an Jiaotong University, Xi'an, P.R. China and The State Key Lab for Manufacturing Systems Engineering, Xi'an, P.R. China;School of Management, Xi'an Jiaotong University, Xi'an, P.R. China and The State Key Lab for Manufacturing Systems Engineering, Xi'an, P.R. China
Venue:
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Year:
2007

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Abstract

Let PG(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 ∈ PG(s, t) = (s,..., u, v,..., t) is defined as a shortest path PG-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) ∈ PG(s, t) whose removal produces a replacement path at node u such that the ratio of the length of PG-e(u, t) to the length of PG(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.