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- W1515693346 abstract "A coterie is a family of subsets such that every pair of subsets has at least one element in common but neither is a subset of the other. A coterie $C$ is said to be non-dominated (ND) if there is no other coterie $D$ such that, for $forall Q in C$, there exists $Q'' in D$ satisfying $Q'' subseteq Q$. We introduce an operator $sigma$, which transforms a ND 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 $sigma$ operations to $C$ at most $|C|+|D|-2$ times. As another application of the $sigma$ operation, we present an incrementally-polynomial-time algorithm for generating all regular ND coteries. We then introduce the concept of ``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 $O(n^3|C|)$ time. We also discuss the structures of optimum coteries with respect to a g-regular function." @default.
- W1515693346 created "2016-06-24" @default.
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- W1515693346 date "1999-07-22" @default.
- W1515693346 modified "2023-09-28" @default.
- W1515693346 title "Transformation of Regular Non-Dominated Coteries" @default.
- W1515693346 hasPublicationYear "1999" @default.
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