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.2016.37
URN: urn:nbn:de:0030-drops-63888
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Dürr, Christoph ; Konrad, Christian ; Renault, Marc

On the Power of Advice and Randomization for Online Bipartite Matching

LIPIcs-ESA-2016-37.pdf (0.6 MB)


While randomized online algorithms have access to a sequence of uniform random bits, deterministic online algorithms with advice have access to a sequence of advice bits, i.e., bits that are set by an all-powerful oracle prior to the processing of the request sequence. Advice bits are at least as helpful as random bits, but how helpful are they? In this work, we investigate the power of advice bits and random bits for online maximum bipartite matching (MBM).

The well-known Karp-Vazirani-Vazirani algorithm [Karp, Vazirani and Vazirani 90] is an optimal randomized (1-1/e)-competitive algorithm for MBM that requires access to Theta(n log n) uniform random bits. We show that Omega(log(1/epsilon) n) advice bits are necessary and O(1/epsilon^5 n) sufficient in order to obtain a (1-epsilon)-competitive deterministic advice algorithm. Furthermore, for a large natural class of deterministic advice algorithms, we prove that Omega(log log log n) advice bits are required in order to improve on the 1/2-competitiveness of the best deterministic online algorithm, while it is known that O(log n) bits are sufficient [Böckenhauer, Komm, Královic and Královic 2011].

Last, we give a randomized online algorithm that uses cn random bits, for integers c >= 1, and a competitive ratio that approaches 1-1/e very quickly as c is increasing. For example if c = 10, then the difference between 1-1/e and the achieved competitive ratio is less than 0.0002.

BibTeX - Entry

  author =	{Christoph D{\"u}rr and Christian Konrad and Marc Renault},
  title =	{{On the Power of Advice and Randomization for Online Bipartite Matching}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{37:1--37:16},
  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 =		{},
  URN =		{urn:nbn:de:0030-drops-63888},
  doi =		{10.4230/LIPIcs.ESA.2016.37},
  annote =	{Keywords: On-line algorithms, Bipartite matching, Randomization}

Keywords: On-line algorithms, Bipartite matching, Randomization
Collection: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016

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