License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2016.46
URN: urn:nbn:de:0030-drops-63584
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6358/
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Goranci, Gramoz ; Henzinger, Monika ; Thorup, Mikkel

Incremental Exact Min-Cut in Poly-logarithmic Amortized Update Time

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LIPIcs-ESA-2016-46.pdf (0.5 MB)

Abstract

We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with ~O(1) amortized time per edge insertion and O(1) query time. This result partially answers an open question posed by Thorup [Combinatorica 2007]. It also stays in sharp contrast to a polynomial conditional lower-bound for the fully-dynamic weighted minimum cut problem. Our algorithm is obtained by combining a recent sparsification technique of Kawarabayashi and Thorup [STOC 2015] and an exact incremental algorithm of Henzinger [J. of Algorithm 1997].

We also study space-efficient incremental algorithms for the minimum cut problem. Concretely, we show that there exists an O(n log n/epsilon^2) space Monte-Carlo algorithm that can process a stream of edge insertions starting from an empty graph, and with high probability, the algorithm maintains a (1+epsilon)-approximation to the minimum cut. The algorithm has ~O(1) amortized update-time and constant query-time.

BibTeX - Entry

@InProceedings{goranci_et_al:LIPIcs:2016:6358,
  author =	{Gramoz Goranci and Monika Henzinger and Mikkel Thorup},
  title =	{{Incremental Exact Min-Cut in Poly-logarithmic Amortized Update Time}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{46:1--46:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Piotr Sankowski and Christos Zaroliagis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6358},
  URN =		{urn:nbn:de:0030-drops-63584},
  doi =		{10.4230/LIPIcs.ESA.2016.46},
  annote =	{Keywords: Dynamic Graph Algorithms, Minimum Cut, Edge Connectivity}
}

Keywords: Dynamic Graph Algorithms, Minimum Cut, Edge Connectivity
Collection: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016

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