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.2016.56
URN: urn:nbn:de:0030-drops-63980
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6398/
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Kliemann, Lasse ; Schielke, Christian ; Srivastav, Anand

A Streaming Algorithm for the Undirected Longest Path Problem

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LIPIcs-ESA-2016-56.pdf (0.6 MB)

Abstract

We present the first streaming algorithm for the longest path problem in undirected graphs. The input graph is given as a stream of edges and RAM is limited to only a linear number of edges at a time (linear in the number of vertices n). We prove a per-edge processing time of O(n), where a naive solution would have required Omega(n^2). Moreover, we give a concrete linear upper bound on the number of bits of RAM that are required.

On a set of graphs with various structure, we experimentally compare our algorithm with three leading RAM algorithms: Warnsdorf (1823), Pohl-Warnsdorf (1967), and Pongrasz (2012). Although conducting only a small constant number of passes over the input, our algorithm delivers competitive results: with the exception of preferential attachment graphs, we deliver at least 71% of the solution of the best RAM algorithm. The same minimum relative performance of 71% is observed over all graph classes after removing the 10% worst cases. This comparison has strong meaning, since for each instance class there is one algorithm that on average delivers at least 84% of a Hamilton path. In some cases we deliver even better results than any of the RAM algorithms.

BibTeX - Entry

@InProceedings{kliemann_et_al:LIPIcs:2016:6398,
  author =	{Lasse Kliemann and Christian Schielke and Anand Srivastav},
  title =	{{A Streaming Algorithm for the Undirected Longest Path Problem}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{56:1--56:17},
  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/2016/6398},
  URN =		{urn:nbn:de:0030-drops-63980},
  doi =		{10.4230/LIPIcs.ESA.2016.56},
  annote =	{Keywords: Streaming Algorithms,   Undirected Longest Path Problem,   Graph Algorithms,   Combinatorial Optimization}
}

Keywords: Streaming Algorithms, Undirected Longest Path Problem, Graph Algorithms, Combinatorial Optimization
Collection: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016

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