The communication complexity of approximate set packing and covering

Noam Nisan*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

40 Scopus citations

Abstract

We consider a setting where k players are each holdingsome collection of subsets of {1..n}. We consider the communication complexity of approximately solvingt wo problems: The cover number: the minimal number of sets (in the union of their collections) whose union is {1...n} and the packing number: the maximum number of sets (in the union of their collections) that are pair-wise disjoint. We prove that while computinga (ln n)-approximation for the cover number and an min(κ,O( √ n))-approximation for the packingn umber can be done with polynomial (in n) amount of communication, getting a (1/2 - ε) log n approximation for the cover number or a better than min(κ, n1/2-ε)-approximation for the packingn umber requires exponential communication complexity.

Original languageAmerican English
Title of host publicationAutomata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings
EditorsPeter Widmayer, Stephan Eidenbenz, Francisco Triguero, Rafael Morales, Ricardo Conejo, Matthew Hennessy
PublisherSpringer Verlag
Pages868-875
Number of pages8
ISBN (Print)3540438645, 9783540438649
DOIs
StatePublished - 2002
Event29th International Colloquium on Automata, Languages, and Programming, ICALP 2002 - Malaga, Spain
Duration: 8 Jul 200213 Jul 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2380 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference29th International Colloquium on Automata, Languages, and Programming, ICALP 2002
Country/TerritorySpain
CityMalaga
Period8/07/0213/07/02

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