A derandomization using min-wise independent permutations

Authors:
Andrei Z. Broder;Moses Charikar;Michael Mitzenmacher
Affiliations:
Altavista Company, 1825 S. Grant Street, San Mateo, CA;Computer Science Department, Stanford University, Stanford, CA;Harvard University, 33 Oxford St., Cambridge, MA
Venue:
Journal of Discrete Algorithms
Year:
2003

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Abstract

Min-wise independence is a recently introduced notion of limited independence, similar in spirit to pairwise independence. The latter has proven essential for the derandomization of many algorithms. Here we show that approximate min-wise independence allows similar uses, by presenting a derandomization of the RNC algorithm for approximate set cover due to S. Rajagopalan and V. Vazirani. We also discuss how to derandomize their set multi-cover and multi-set multi-cover algorithms in restricted cases. The multi-cover case leads us to discuss the concept of k-minima-wise independence, a natural counterpart to k-wise independence.