Efficient conditional expectation algorithms for constructing hash families

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

3 Citations (Scopus)

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages144-155
Number of pages12
Volume7056 LNCS
DOIs
StatePublished - 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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Conditional Expectation
Set Cover
Polynomials
Covering Array
Family
Polynomial time
NP-complete problem
Formulation
Range of data

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Colbourn, C. (2011). Efficient conditional expectation algorithms for constructing hash families. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7056 LNCS, 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

Efficient conditional expectation algorithms for constructing hash families. / Colbourn, Charles.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7056 LNCS 2011. p. 144-155 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7056 LNCS).

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

Colbourn, C 2011, Efficient conditional expectation algorithms for constructing hash families. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7056 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7056 LNCS, pp. 144-155, 22nd International Workshop on Combinatorial Algorithms, IWOCA 2011, Vancouver, BC, Canada, 7/20/11. https://doi.org/10.1007/978-3-642-25011-8_12
Colbourn C. Efficient conditional expectation algorithms for constructing hash families. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7056 LNCS. 2011. p. 144-155. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-25011-8_12
Colbourn, Charles. / Efficient conditional expectation algorithms for constructing hash families. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7056 LNCS 2011. pp. 144-155 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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