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Isolating Cuts, (Bi-)Submodularity, and Faster Algorithms for Connectivity

Authors Chandra Chekuri, Kent Quanrud



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Chandra Chekuri
  • University of Illinois at Urbana-Champaign, IL, USA
Kent Quanrud
  • Purdue University, West Lafayette, IN, USA

Acknowledgements

We thank the reviewers for their helpful comments.

Cite AsGet BibTex

Chandra Chekuri and Kent Quanrud. Isolating Cuts, (Bi-)Submodularity, and Faster Algorithms for Connectivity. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 50:1-50:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ICALP.2021.50

Abstract

Li and Panigrahi [Jason Li and Debmalya Panigrahi, 2020], 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • cuts
  • vertex connectivity
  • hypergraphs
  • fast algorithms
  • submodularity
  • bisumodularity
  • lattices
  • isolating cuts
  • element connectivity

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