# Efficient Algorithms for Listing k Disjoint st-Paths in Graphs

Abstract : Given a connected graph G of m edges and n vertices, we consider the basic problem of listing all the choices of k vertex-disjoint st-paths, for any two input vertices s, t of G and a positive integer k. Our algorithm takes O(m) time per solution, using O(m) space and requiring O(F k (G)) setup time, where $F k (G) = O(m min{k, n 2/3 log n, √ m log n})$ is the cost of running a max-flow algorithm on G to compute a flow of size k. The proposed techniques are simple and apply to other related listing problems discussed in the paper.
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Conference papers
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Cited literature [18 references]

https://hal.inria.fr/hal-01964712
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Submitted on : Sunday, December 23, 2018 - 12:29:45 PM
Last modification on : Tuesday, February 26, 2019 - 10:54:02 AM
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### Citation

Roberto Grossi, Andrea Marino, Luca Versari. Efficient Algorithms for Listing k Disjoint st-Paths in Graphs. LATIN 2018 - 13th Latin American Symposium on Theoretical Informatics, Apr 2018, Buenos Aires, Argentina. pp.544-557, ⟨10.1007/978-3-319-77404-6_40⟩. ⟨hal-01964712⟩

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