TY - GEN

T1 - Randomized post-optimization for t-restrictions

AU - Colbourn, Charles

AU - Nayeri, Peyman

N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - covering array

KW - disjunct matrix

KW - frameproof code

KW - hash family

UR - http://www.scopus.com/inward/record.url?scp=84875994354&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-36899-8_30

DO - 10.1007/978-3-642-36899-8_30

M3 - Conference contribution

AN - SCOPUS:84875994354

SN - 9783642368981

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 597

EP - 608

BT - Information Theory, Combinatorics, and Search Theory

PB - Springer Verlag

ER -