Isolating Cuts, (Bi-)Submodularity, and Faster Algorithms for Connectivity
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.
cuts
vertex connectivity
hypergraphs
fast algorithms
submodularity
bisumodularity
lattices
isolating cuts
element connectivity
Theory of computation~Graph algorithms analysis
50:1-50:20
Track A: Algorithms, Complexity and Games
https://arxiv.org/abs/2103.12908
We thank the reviewers for their helpful comments.
Chandra
Chekuri
Chandra Chekuri
University of Illinois at Urbana-Champaign, IL, USA
http://chekuri.cs.illinois.edu/
Supported in part by NSF grants CCF-1910149 and CCF-1907937.
Kent
Quanrud
Kent Quanrud
Purdue University, West Lafayette, IN, USA
https://www.kentquanrud.com/
10.4230/LIPIcs.ICALP.2021.50
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Chandra Chekuri and Kent Quanrud
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