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International Computing and Combinatorics Conference

COCOON 2018: Computing and Combinatorics pp 14–25Cite as

Exact Algorithms for Finding Partial Edge-Disjoint Paths

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10976))

Abstract

For a given graph G with non-negative integral edge length, a pair of distinct vertices s and t, and a given positive integer \(\delta \), the k partial edge-disjoint shortest path (kPESP)problem aims to compute k shortest st-paths among which there are at most \(\delta \) edges shared by at least two paths. In this paper, we first present an exact algorithm with a runtime \(O(mn\log _{(1+m/n)}n+\delta n^{2})\) for kPESP with \(k=2\). Then observing the algorithm can not be extended for general k, we propose another algorithm with a runtime \(O(\delta 2^{k}n^{k+1})\) in DAGs based on graph transformation. In addition, we show the algorithm can be extended to kPESP with an extra edge congestion constraint that each edge can be shared by at most C paths for a given integer \(C\le k\).

The research is supported by Natural Science Foundation of China (Nos. 61772005, 61300025) and Natural Science Foundation of Fujian Province (No. 2017J01753).

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Notes

  1. 1.

    Note that the algorithm was previously extended to solve many other related problems including [3, 19].

  2. 2.

    Following the tradition in mathematics, the notation \([n]^{+}\) denotes the set \(\{1,\,\dots ,\,n\}\).

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, China

    Yunyun Deng & Longkun Guo

  2. College of Physics and Information Engineering, Fuzhou University, Fuzhou, China

    Peihuang Huang

Authors
  1. Yunyun Deng
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  2. Longkun Guo
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  3. Peihuang Huang
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Corresponding author

Correspondence to Longkun Guo .

Editor information

Editors and Affiliations

  1. City University of Hong Kong, Hong Kong, China

    Lusheng Wang

  2. Shandong University, Jinan, China

    Daming Zhu

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Deng, Y., Guo, L., Huang, P. (2018). Exact Algorithms for Finding Partial Edge-Disjoint Paths. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-94776-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94775-4

  • Online ISBN: 978-3-319-94776-1

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