Tabu search for covering arrays using permutation vectors

A covering array  CA(N;t,k,v)CA(N;t,k,v) is an N×kN×k array, in which in every N×tN×t subarray, each of the vtvt possible t  -tuples over vv symbols occurs at least once. The parameter t is the strength   of the array. Covering arrays have a wide range of applications for experimental screening designs, particularly for software interaction testing. A compact representation of certain covering arrays employs “permutation vectors” to encode vt×1vt×1 subarrays of the covering array so that a covering perfect hash family whose entries correspond to permutation vectors yields a covering array. We introduce a method for effective search for covering arrays of this type using tabu search. Using this technique, improved covering arrays of strength 3, 4 and 5 have been found, as well as the first arrays of strength 6 and 7 found by computational search.