Isolating cuts, (Bi-)submodularity, and faster algorithms for connectivity

Chandra Chekuri, Kent Quanrud

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Li and Panigrahi [37], in recent work, obtained the first deterministic algorithm for the global minimum cut of a weighted undirected graph that runs in time o(mn). They introduced an elegant and powerful technique to find isolating cuts for a terminal set in a graph via a small number of s-t minimum cut computations. In this paper we generalize their isolating cut approach to the abstract setting of symmetric bisubmodular functions (which also capture symmetric submodular functions). Our generalization to bisubmodularity is motivated by applications to element connectivity and vertex connectivity. Utilizing the general framework and other ideas we obtain significantly faster randomized algorithms for computing global (and subset) connectivity in a number of settings including hypergraphs, element connectivity and vertex connectivity in graphs, and for symmetric submodular functions.

Original languageEnglish (US)
Title of host publication48th International Colloquium on Automata, Languages, and Programming, ICALP 2021
EditorsNikhil Bansal, Emanuela Merelli, James Worrell
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771955
DOIs
StatePublished - Jul 1 2021
Event48th International Colloquium on Automata, Languages, and Programming, ICALP 2021 - Virtual, Glasgow, United Kingdom
Duration: Jul 12 2021Jul 16 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume198
ISSN (Print)1868-8969

Conference

Conference48th International Colloquium on Automata, Languages, and Programming, ICALP 2021
Country/TerritoryUnited Kingdom
CityVirtual, Glasgow
Period7/12/217/16/21

Keywords

  • Bisumodularity
  • Cuts
  • Element connectivity
  • Fast algorithms
  • Hypergraphs
  • Isolating cuts
  • Lattices
  • Submodularity
  • Vertex connectivity

ASJC Scopus subject areas

  • Software

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