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How Vulnerable is an Undirected Planar Graph with Respect to Max Flow

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Algorithms and Complexity (CIAC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13898))

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Abstract

We study the problem of computing the vitality of edges and vertices with respect to the st-max flow in undirected planar graphs, where the vitality of an edge/vertex is the st-max flow decrease when the edge/vertex is removed from the graph. This allows us to establish the vulnerability of the graph with respect to the st-max flow.

We give efficient algorithms to compute an additive guaranteed approximation of the vitality of edges and vertices in planar undirected graphs. We show that in the general case high vitality values are well approximated in time close to the time currently required to compute st-max flow \(O(n\log \log n)\). We also give improved, and sometimes optimal, results in the case of integer capacities. All our algorithms work in O(n) space.

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Authors and Affiliations

  1. Dipartimento di Scienze Statistiche, Sapienza Università di Roma, p.le Aldo Moro 5, 00185, Rome, Italy

    Lorenzo Balzotti & Paolo G. Franciosa

Authors
  1. Lorenzo Balzotti
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  2. Paolo G. Franciosa
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Correspondence to Lorenzo Balzotti .

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  1. University of Cyprus, Nicosia, Cyprus

    Marios Mavronicolas

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Balzotti, L., Franciosa, P.G. (2023). How Vulnerable is an Undirected Planar Graph with Respect to Max Flow. In: Mavronicolas, M. (eds) Algorithms and Complexity. CIAC 2023. Lecture Notes in Computer Science, vol 13898. Springer, Cham. https://doi.org/10.1007/978-3-031-30448-4_7

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  • DOI: https://doi.org/10.1007/978-3-031-30448-4_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-30447-7

  • Online ISBN: 978-3-031-30448-4

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