Abstract
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 allpowerful 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 wellknown KarpVaziraniVazirani algorithm [Karp, Vazirani and Vazirani 90] is an optimal randomized (11/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 (1epsilon)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 1/2competitiveness 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 11/e very quickly as c is increasing. For example if c = 10, then the difference between 11/e and the achieved competitive ratio is less than 0.0002.
BibTeX  Entry
@InProceedings{drr_et_al:LIPIcs:2016:6388,
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 = {37:137:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770156},
ISSN = {18688969},
year = {2016},
volume = {57},
editor = {Piotr Sankowski and Christos Zaroliagis},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6388},
URN = {urn:nbn:de:0030drops63888},
doi = {10.4230/LIPIcs.ESA.2016.37},
annote = {Keywords: Online algorithms, Bipartite matching, Randomization}
}
Keywords: 

Online algorithms, Bipartite matching, Randomization 
Seminar: 

24th Annual European Symposium on Algorithms (ESA 2016) 
Issue Date: 

2016 
Date of publication: 

18.08.2016 