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/
Jindal, Gorav ;
Kolev, Pavel ;
Peng, Richard ;
Sawlani, Saurabh
Density Independent Algorithms for Sparsifying k-Step Random Walks
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: |
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random walks, graph sparsification, spectral graph theory, effective resistances |
Collection: |
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017) |
Issue Date: |
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2017 |
Date of publication: |
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11.08.2017 |