Randomized post-optimization for t-restrictions

Charles Colbourn, Peyman Nayeri

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

1 Scopus citations

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 publicationInformation Theory, Combinatorics, and Search Theory
Subtitle of host publicationIn Memory of Rudolf Ahlswede
EditorsHarout Aydinian, Christian Deppe, Ferdinando Cicalese
Pages597-608
Number of pages12
DOIs
StatePublished - Apr 15 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7777
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

    Fingerprint

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Colbourn, C., & Nayeri, P. (2013). Randomized post-optimization for t-restrictions. In H. Aydinian, C. Deppe, & F. Cicalese (Eds.), Information Theory, Combinatorics, and Search Theory: In Memory of Rudolf Ahlswede (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