Efficient conditional expectation algorithms for constructing hash families

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

Greedy methods for solving set cover problems provide a guarantee on how close the solution is to optimal. Consequently they have been widely explored to solve set cover problems arising in the construction of various combinatorial arrays, such as covering arrays and hash families. In these applications, however, a naive set cover formulation lists a number of candidate sets that is exponential in the size of the array to be produced. Worse yet, even if candidate sets are not listed, finding the 'best' candidate set is NP-hard. In this paper, it is observed that one does not need a best candidate set to obtain the guarantee - an average candidate set will do. Finding an average candidate set can be accomplished using a technique employing the method of conditional expectations for a wide range of set cover problems arising in the construction of hash families. This yields a technique for constructing hash families, with a wide variety of properties, in time polynomial in the size of the array produced.

Original languageEnglish (US)
Title of host publicationCombinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers
Pages144-155
Number of pages12
DOIs
StatePublished - Nov 28 2011
Event22nd International Workshop on Combinatorial Algorithms, IWOCA 2011 - Vancouver, BC, Canada
Duration: Jul 20 2011Jul 22 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7056 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other22nd International Workshop on Combinatorial Algorithms, IWOCA 2011
CountryCanada
CityVancouver, BC
Period7/20/117/22/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Colbourn, C. (2011). Efficient conditional expectation algorithms for constructing hash families. In Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers (pp. 144-155). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7056 LNCS). https://doi.org/10.1007/978-3-642-25011-8_12