Covering Arrays Of Strength Research Articles

Covering arrays of strength three from extended permutation vectors

A covering array $$\text{ CA }(N;t,k,v)$$ is an $$N\times k$$ array such that in every $$N\times t$$ subarray each possible t-tuple over a v-set appears as a row of the subarray at least once. The integers t and v are respectively the strength and the order of the covering array. Let v be a prime power and let $${\mathbb {F}}_v$$ denote the finite field with v elements. In this work the original concept of permutation vectors generated by a $$(t-1)$$ -tuple over $${\mathbb {F}}_v$$ is extended to vectors generated by a t-tuple over $${\mathbb {F}}_v$$ . We call these last vectors extended permutation vectors (EPVs). For every prime power v, a covering perfect hash family $$\text{ CPHF }(2;v^2-v+3,v^3,3)$$ is constructed from EPVs given by subintervals of a linear feedback shift register sequence over $${\mathbb {F}}_v$$ . When $$v\in \{7,9,11,13,16,17,19,23,25\}$$ the covering array $$\text{ CA }(2v^3-v;3,v^2-v+3,v)$$ generated by $$\text{ CPHF }(2;v^2-v+3,v^3,3)$$ has less rows than the best-known covering array with strength three, $$v^2-v+3$$ columns, and order v. CPHFs formed by EPVs are also constructed using simulated annealing; in this case the results improve the size of eighteen covering arrays of strength three.

Augmentation of Covering Arrays of Strength Two

Augmentation is an operation to increase the number of symbols in a covering array, without unnecessarily increasing the number of rows. For covering arrays of strength two, one type of augmentation forms a covering array on $$v$$v symbols from one on $$v-1$$v-1 symbols together with $$v-1$$v-1 covering arrays each on two symbols. A careful analysis of the structure of the optimal binary covering arrays underlies an augmentation operation that reduces the number of rows required. Consequently a number of covering array numbers are improved.

Covering arrays of strength 3 and 4 from holey difference matrices

A covering array CA(N; t, k, v) is an N × k array with entries from a set X of v symbols such that every N × t sub-array contains all t-tuples over X at least once, where t is the strength of the array. The minimum size N for which a CA(N; t, k, v) exists is called the covering array number and denoted by CAN(t, k, v). Covering arrays are used in experiments to screen for interactions among t-subsets of k components. One of the main problems on covering arrays is to construct a CA(N; t, k, v) for given parameters (t, k, v) so that N is as small as possible. In this paper, we present some constructions of covering arrays of strengths 3 and 4 via holey difference matrices with prescribed properties. As a consequence, some of known bounds on covering array number are improved. In particular, it is proved that (1) CAN(3, 5, 2v) ? 2v 2(4v + 1) for any odd positive integer v with gcd(v, 9) ? 3; (2) CAN(3, 6, 6p) ? 216p 3 + 42p 2 for any prime p > 5; and (3) CAN(4, 6, 2p) ? 16p 4 + 5p 3 for any prime p ? 1 (mod 4) greater than 5.

Covering arrays of higher strength from permutation vectors

AbstractA covering array CA(N;t,k,v) is an N × k array such that every N × t sub‐array contains all t‐tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t‐sets of component interactions. We introduce a combinatorial technique for their construction, focussing on covering arrays of strength 3 and 4. With a computer search, covering arrays with improved parameters have been found. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 202–213, 2006