Explicit construction of exponential sized families of K-independent sets
Discrete Mathematics
Randomized algorithms
Theoretical Computer Science
The AETG System: An Approach to Testing Based on Combinatorial Design
IEEE Transactions on Software Engineering
The density algorithm for pairwise interaction testing: Research Articles
Software Testing, Verification & Reliability
On generalized separating hash families
Journal of Combinatorial Theory Series A
A bound on the size of separating hash families
Journal of Combinatorial Theory Series A
A density-based greedy algorithm for higher strength covering arrays
Software Testing, Verification & Reliability
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
On greedy algorithms in coding theory
IEEE Transactions on Information Theory - Part 1
Strengthening hash families and compressive sensing
Journal of Discrete Algorithms
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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.