Upper Bounds for Covering Designs by SimulatedAnnealingKari
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چکیده
A t ? (v; m; k;) covering design is a pair (X; A), where X is a set of v elements (called points) and A is a multiset of k-subsets of X (called blocks), such that every m-subset of X intersects at least members of A in at least t points. It is required that v k t and v m t. Such a covering design gives an upper bound on C (v; m; k; t), the number of blocks in a minimal t ? (v; m; k;) covering design. In this paper it is shown how simulated annealing, a probabilistic method for solving combinatorial optimization problems, can be used to construct covering designs. Implementation of this method is discussed. The method is used to calculate new upper bounds on C 1 (v; t; k; t) for k 9, v 13. A new exact value, C 1 (11; 4; 6; 4) = 32, is obtained.
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تاریخ انتشار 1993