Search problems
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
Explicit constructions of separating hash families from algebraic curves over finite fields
Designs, Codes and Cryptography
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Randomized Postoptimization of Covering Arrays
Combinatorial Algorithms
Some Improved Bounds for Secure Frameproof Codes and Related Separating Hash Families
IEEE Transactions on Information Theory
Strengthening hash families and compressive sensing
Journal of Discrete Algorithms
Randomized post-optimization of covering arrays
European Journal of Combinatorics
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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.