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.SoCG.2016.22
URN: urn:nbn:de:0030-drops-59149
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5914/
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Borradaile, Glencora ; Eppstein, David ; Nayyeri, Amir ; Wulff-Nilsen, Christian

All-Pairs Minimum Cuts in Near-Linear Time for Surface-Embedded Graphs

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LIPIcs-SoCG-2016-22.pdf (0.6 MB)

Abstract

For an undirected n-vertex graph G with non-negative edge-weights, we consider the following type of query: given two vertices s and t in G, what is the weight of a minimum st-cut in G? We solve this problem in preprocessing time O(n log^3 n) for graphs of bounded genus, giving the first sub-quadratic time algorithm for this class of graphs. Our result also improves by a logarithmic factor a previous algorithm by Borradaile, Sankowski and Wulff-Nilsen (FOCS 2010) that applied only to planar graphs. Our algorithm constructs a Gomory-Hu tree for the given graph, providing a data structure with space O(n) that can answer minimum-cut queries in constant time. The dependence on the genus of the input graph in our preprocessing time is 2^{O(g^2)}.

BibTeX - Entry

@InProceedings{borradaile_et_al:LIPIcs:2016:5914,
  author =	{Glencora Borradaile and David Eppstein and Amir Nayyeri and Christian Wulff-Nilsen},
  title =	{{All-Pairs Minimum Cuts in Near-Linear Time for Surface-Embedded Graphs}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{S{\'a}ndor Fekete and Anna Lubiw},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5914},
  URN =		{urn:nbn:de:0030-drops-59149},
  doi =		{10.4230/LIPIcs.SoCG.2016.22},
  annote =	{Keywords: minimum cuts, surface-embedded graphs, Gomory-Hu tree}
}

Keywords: minimum cuts, surface-embedded graphs, Gomory-Hu tree
Collection: 32nd International Symposium on Computational Geometry (SoCG 2016)
Issue Date: 2016
Date of publication: 10.06.2016

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