On Rooted k-Connectivity Problems in Quasi-bipartite Digraphs

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We consider the directed Rooted Subset k -Edge-Connectivity problem: given a digraph G= (V, E) with edge costs, a set T⊂ V of terminals, a root node r, and an integer k, find a min-cost subgraph of G that contains k edge disjoint rt-paths for all t∈ T. The case when every edge of positive cost has head in T admits a polynomial time algorithm due to Frank [9], and the case when all positive cost edges are incident to r is equivalent to the k -Multicover problem. Recently, Chan et al. [2] obtained ratio O(ln kln | T| ) for quasi-bipartite instances, when every edge in G has an end (tail and/or head) in T+ r. We give a simple proof for the same ratio for a more general problem of covering an arbitrary T-intersecting supermodular set function by a minimum cost edge set, and for the case when only every positive cost edge has an end in T+ r.

Original languageEnglish
Title of host publicationComputer Science – Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings
EditorsRahul Santhanam, Daniil Musatov
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages10
ISBN (Print)9783030794156
StatePublished - 2021
Event16th International Computer Science Symposium in Russia, CSR 2021 - Sochi, Russian Federation
Duration: 28 Jun 20212 Jul 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12730 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Computer Science Symposium in Russia, CSR 2021
Country/TerritoryRussian Federation

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


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