Efficient generation of all regular non-dominated coteries

  • Authors:
  • Kazuhisa Makino;Tiko Kameda

  • Affiliations:
  • Department of Systems and Human Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, 560-8531, Japan;School of Computing Science, Faculty of Applied Sciences, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada

  • Venue:
  • Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
  • Year:
  • 2000

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Abstract

A coterie is a family of subsets such that every pair of subsets in it has at least one element in common but neither is a subset of the other. We introduce an operator &sgr;, which transforms a ND (non-dominated; see the Introduction for definition) coterie to another ND coterie. A “regular” coterie is a natural generalization of a “vote-assignable” coterie, which is used in some practical applications. We show that any regular ND coterie C can be transformed to any other regular ND coterie D by judiciously applying &sgr; operations to C at most |C| + |D| - 2 times.As another application of the &sgr; operation, we present an incrementally-polynomial-time algorithm for generating all regular ND coteries. We then introduce the concept of a “g-regular” function, as a generalization of availability. We show how to construct an optimum coterie C with respect to a g-regular function in O(n3|C|) time.