On the covering of t-sets with (t+1)-sets: C(9,5,4) and C(10,6,5)
Discrete Mathematics
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Optimal covering designs: complexity results and new bounds
Discrete Applied Mathematics - Fun with algorithms 2 (FUN 2001)
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In this paper we introduce and study the problem of computing optimal lottery schemes in the case in which a weight function is specified over the domain set. In particular, we prove that if the number of required hits is equal to 1, then the problem is solvable in polynomial time, and that if the number of required hits is equal to t, then the problem admits a polynomial-time (k t)-approximation algorithm, where k denotes the size of the tuples to be hit.