Optimal covering designs: complexity results and new bounds

• Published in: Discrete Applied Mathematics Vol. 144; no. 3; pp. 281 - 290
• Main Authors: Crescenzi, Pilu, Montecalvo, Federico, Rossi, Gianluca
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Lausanne Elsevier B.V 15.12.2004; Amsterdam Elsevier; New York, NY
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Approximation algorithm; Combinatorial design; Combinatorics; Combinatorics. Ordered structures; Computational complexity; Computer science; control theory; systems; Covering design; Designs and configurations; Exact sciences and technology; Mathematics; Sciences and techniques of general use; Theoretical computing; Covering design; Combinatorial design; Approximation algorithm; Computational complexity; Upper bound; Computer theory; Covering problem; Set covering; Optimal design(statistics); Computing; Combinatorics
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/j.dam.2003.11.006

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 | T| -approximable (where T denotes the collection of sets to be covered) and it cannot be approximated within a factor smaller than log | T| , unless P= N P . 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.