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.APPROX-RANDOM.2017.14
URN: urn:nbn:de:0030-drops-75638
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7563/
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Jindal, Gorav ; Kolev, Pavel ; Peng, Richard ; Sawlani, Saurabh

Density Independent Algorithms for Sparsifying k-Step Random Walks

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LIPIcs-APPROX-RANDOM-2017-14.pdf (0.6 MB)

Abstract

We give faster algorithms for producing sparse approximations of the transition matrices of k-step random walks on undirected and weighted graphs. These transition matrices also form graphs, and arise as intermediate objects in a variety of graph algorithms. Our improvements are based on a better understanding of processes that sample such walks, as well as tighter bounds on key weights underlying these sampling processes. On a graph with n vertices and m edges, our algorithm produces a graph with about nlog(n) edges that approximates the k-step random walk graph in about m + k^2 nlog^4(n) time. In order to obtain this runtime bound, we also revisit "density independent" algorithms for sparsifying graphs whose runtime overhead is expressed only in terms of the number of vertices.

BibTeX - Entry

@InProceedings{jindal_et_al:LIPIcs:2017:7563,
  author =	{Gorav Jindal and Pavel Kolev and Richard Peng and Saurabh Sawlani},
  title =	{{Density Independent Algorithms for Sparsifying k-Step Random Walks}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7563},
  URN =		{urn:nbn:de:0030-drops-75638},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.14},
  annote =	{Keywords: random walks, graph sparsification, spectral graph theory, effective resistances}
}

Keywords: random walks, graph sparsification, spectral graph theory, effective resistances
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Issue Date: 2017
Date of publication: 11.08.2017

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