Quasi-Polynomial Local Search for Restricted Max-Min Fair Allocation
2012 (English)In: ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I, Springer Berlin/Heidelberg, 2012, 726-737 p.Conference paper (Refereed)
The restricted max-min fair allocation problem (also known as the restricted Santa Claus problem) is one of few problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, Asadpour et al.  proved that a certain configuration LP can be used to estimate the optimal value within a factor 1/(4+ε), for any ε>0, but at the same time it is not known how to efficiently find a solution with a comparable performance guarantee.
A natural question that arises from their work is if the difference between these guarantees is inherent or because of a lack of suitable techniques. We address this problem by giving a quasi-polynomial approximation algorithm with the mentioned performance guarantee. More specifically, we modify the local search of  and provide a novel analysis that lets us significantly improve the bound on its running time: from 2O(n) to nO(logn). Our techniques also have the interesting property that although we use the rather complex configuration LP in the analysis, we never actually solve it and therefore the resulting algorithm is purely combinatorial.
Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2012. 726-737 p.
IdentifiersURN: urn:nbn:se:kth:diva-111483DOI: 10.1007/978-3-642-31594-7_61ISI: 000342761000061ScopusID: 2-s2.0-84883756966ISBN: 978-3-642-31593-0OAI: oai:DiVA.org:kth-111483DiVA: diva2:586621
39th international colloquium conference on Automata, Languages, and Programming, ICALP 2012
QC 201301142013-01-142013-01-122015-06-11Bibliographically approved