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Generating and approximating nondominated coteries

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2 Author(s)
Bioch, J.C. ; Dept. of Comput. Sci., Erasmus Univ., Rotterdam, Netherlands ; Ibaraki, T.

A coterie, which is used to realize mutual exclusion in a distributed system is a family C of incomparable subsets such that every pair of subsets in C has at least one element in common. Associate with a family of subsets C a positive (i.e., monotone) Boolean function fc such that fc(x)=1 if the Boolean vector x is equal to or greater than the characteristic vector of some subset in C, and 0 otherwise. It is known that C is a coterie if and only if fc is dual-minor, and is a nondominated (ND) coterie if and only if fc is self-dual. We introduce an operator ρ, which transforms a positive self-dual function into another positive self-dual function, and the concept of almost-self-duality, which is a close approximation to self-duality and can be checked in polynomial time (the complexity of checking positive self-duality is currently unknown). After proving several interesting properties of them, we propose a simple algorithm to check whether a given positive function is self-dual or not. Although this is not a polynomial algorithm, it is practically efficient in most cases. Finally, we present an incrementally polynomial algorithm that generates all positive self-dual functions (ND coteries) by repeatedly applying p operations. Based on this algorithm, all ND coteries of up to seven variables are computed

Published in:

Parallel and Distributed Systems, IEEE Transactions on  (Volume:6 ,  Issue: 9 )

Date of Publication:

Sep 1995

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