TY - GEN
T1 - Efficient conditional expectation algorithms for constructing hash families
AU - Colbourn, Charles
PY - 2011/11/28
Y1 - 2011/11/28
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-642-25011-8_12
DO - 10.1007/978-3-642-25011-8_12
M3 - Conference contribution
AN - SCOPUS:81855185027
SN - 9783642250101
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 144
EP - 155
BT - Combinatorial Algorithms - 22nd International Workshop, IWOCA 2011, Revised Selected Papers
T2 - 22nd International Workshop on Combinatorial Algorithms, IWOCA 2011
Y2 - 20 July 2011 through 22 July 2011
ER -