Randomized post-optimization for t-restrictions

Charles Colbourn, Peyman Nayeri

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

1 Citation (Scopus)

Abstract

Search, test, and measurement problems in sparse domains often require the construction of arrays in which every t or fewer columns satisfy a simply stated combinatorial condition. Such t-restriction problems often ask for the construction of an array satisfying the t-restriction while having as few rows as possible. Combinatorial, algebraic, and probabilistic methods have been brought to bear for specific t-restriction problems; yet in most cases they do not succeed in constructing arrays with a number of rows near the minimum, at least when the number of columns is small. To address this, an algorithmic method is proposed that, given an array satisfying a t-restriction, attempts to improve the array by removing rows. The key idea is to determine the necessity of the entry in each cell of the array in meeting the t-restriction, and repeatedly replacing unnecessary entries, with the goal of producing an entire row of unnecessary entries. Such a row can then be deleted, improving the array, and the process can be iterated. For certain t-restrictions, it is shown that by determining conflict graphs, entries that are necessary can nonetheless be changed without violating the t-restriction. This permits a richer set of ways to improve the arrays. The efficacy of these methods is demonstrated via computational results.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages597-608
Number of pages12
Volume7777
DOIs
StatePublished - 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7777
ISSN (Print)03029743
ISSN (Electronic)16113349

Fingerprint

Restriction
Optimization
Probabilistic Methods
Algebraic Methods
Computational Results
Efficacy
Entire
Necessary
Cell
Graph in graph theory

Keywords

  • covering array
  • disjunct matrix
  • frameproof code
  • hash family

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Colbourn, C., & Nayeri, P. (2013). Randomized post-optimization for t-restrictions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7777, pp. 597-608). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7777). https://doi.org/10.1007/978-3-642-36899-8-30

Randomized post-optimization for t-restrictions. / Colbourn, Charles; Nayeri, Peyman.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7777 2013. p. 597-608 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7777).

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

Colbourn, C & Nayeri, P 2013, Randomized post-optimization for t-restrictions. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7777, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7777, pp. 597-608. https://doi.org/10.1007/978-3-642-36899-8-30
Colbourn C, Nayeri P. Randomized post-optimization for t-restrictions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7777. 2013. p. 597-608. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-36899-8-30
Colbourn, Charles ; Nayeri, Peyman. / Randomized post-optimization for t-restrictions. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7777 2013. pp. 597-608 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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