Chapter

LATIN '92

Volume 583 of the series Lecture Notes in Computer Science pp 130-138

Date:

Average case analysis of a greedy algorithm for the minimum hitting set problem

  • W. Fernandez de la VegaAffiliated withUniversité de Paris-XI
  • , V. Th. PaschosAffiliated withUniversité de Paris-XICERMSEM, Université de Paris I-Sorbonne
  • , R. SaadAffiliated withUniversité de Paris-XI

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Abstract

Let k be fixed. Let n and m denote integers and C = {C 1,...,C m} a family of m subsets drawn from an n-element set C. A subset H \(\subseteq\) C is a hitting set for the family C if H has a non-empty intersection with each element of this family and the minimum hitting set problem is that of finding a hitting set of minimum cardinality. The purpose of this paper is to study the efficiency of a natural greedy algorithm for the approximate solution of the minimum hitting set probl em when C is a random family of k-element subsets, k fixed, and when n and m tend to ∞ with \(\tfrac{m}{n}\) = α, a fixed constant.