Exact Algorithms for Finding Partial Edge-Disjoint Paths

Deng, Yunyun; Guo, Longkun; Huang, Peihuang

doi:10.1007/978-3-319-94776-1_2

Cited by 3 publications

(1 citation statement)

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“…Similarly, the k partially edge-disjoint path problem (kP ESP ) computes the shortest set of k paths connecting s and t such that at most δ edges are shared by at least two paths. For k = 2, Yunyun et al [6] introduced an exact algorithm with a runtime O(mn log (1+m/n) n + δn 2 ). In the above works, δ > 0 was referred to as the disjointness factor.…”

Section: Related Workmentioning

confidence: 99%

Partially Disjoint k Shortest Paths

Dinitz¹,

Kumar²,

Schieber³

2022

Preprint

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A solution of the k shortest paths problem may output paths that are identical up to a single edge. On the other hand, a solution of the k independent shortest paths problem consists of paths that share neither an edge nor an intermediate node. We investigate the case in which the number of edges that are not shared among any two paths in the output k-set is a parameter. We study two main directions: exploring near-shortest paths and exploring exactly shortest paths. We assume that the weighted graph G = (V, E, w) has no parallel edges and that the edge lengths (weights) are positive. Our results are also generalized to the cases of k shortest paths where there are several weights per edge, and the results should take into account the multi-criteria prioritized weight.

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Section: Related Workmentioning

confidence: 99%