A completion of Lu's determination of the spectrum of large sets of disjoint Steiner Triple systems
Journal of Combinatorial Theory Series A
On the covering of t-sets with (t+1)-sets: C(9,5,4) and C(10,6,5)
Discrete Mathematics
Introduction to the theory of complexity
Introduction to the theory of complexity
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
The minimum likely column cover problem
Information Processing Letters
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In this paper we investigate the problem of computing optimal lottery schemes. From a computational complexity point of view, we prove that the variation of this problem in which the sets to be covered are specified in the input is log |I|-approximable (where I denotes the collection of sets to be covered) and it cannot be approximated within a factor smaller than log |I|, unless P = NP. From a combinatorial point of view, we propose new constructions based on the combination of the partitioning technique and of known results regarding the construction of sets of coverings. By means of this combination we will be able to improve several upper bounds on the cardinality of optimal lottery schemes.