Áååë Ì Blockinòò Blockin

A oterie is a family of subsets su h that every pair of subsets has at least one element in ommon but neither is a subset of the other. A oterie C is said to be non-dominated (ND) if there is no other oterie D su h that, for 8Q 2 C, there exists Q0 2 D satisfying Q0 Q. We introdu e an operator , whi h transforms a ND oterie to another ND oterie. A regular oterie is a natural generalization of a \vote-assignable" oterie, whi h is used in some pra ti al appli ations. We show that any \regular" ND oterie C an be transformed to any other regular ND oterie D by judi iously applying operations to C at most jCj+ jDj 2 times. As another appli ation of the operation, we present an in rementally-polynomial-time algorithm for generating all regular ND oteries. We then introdu e the on ept of \g-regular" fun tion, as a generalization of availability. We show how to onstru t an optimum oterie C with respe t to a g-regular fun tion in O(n3jCj) time. We also dis uss the stru tures of optimum oteries with respe t to a g-regular fun tion.