Related papers: Partial Covering Arrays: Algorithms and Asymptotic…
A covering array CA(N; t; k; v) is an N x k array on v symbols such that every N x t subarray contains as a row each t-tuple over the v symbols at least once. The minimum N for which a CA(N; t; k; v) exists is called the covering array…
A covering array $CA(N; t,k,v)$ is an $N \times k$ array $A$ whose each cell takes a value for a $v$-set $V$ called an alphabet. Moreover, the set $V^t$ is contained in the set of rows of every $N \times t$ subarray of $A$. The parameter…
A \emph{covering array} is an $N \times k$ array of elements from a $v$-ary alphabet such that every $N \times t$ subarray contains all $v^t$ tuples from the alphabet of size $t$ at least $\lambda$ times; this is denoted as $\CA_\lambda(N;…
Given a set $S$ of $v \ge 2$ symbols, and integers $k \ge t \ge 2$ and $N \ge 1$, an $N \times k$ array $A \in S^{N \times k}$ is an $(N; t, k, v)$-covering array if all sequences in $S^t$ appear as rows in every $N \times t$ subarray of…
A covering array $\rm{CA}(N;t,k,v)$ of strength $t$ is an $N \times k$ array of symbols from an alphabet of size $v$ such that in every $N \times t$ subarray, every $t$-tuple occurs in at least one row. A covering array is \emph{optimal} if…
Covering arrays find important application in software and hardware interaction testing. For practical applications it is useful to determine or bound the minimum number of rows, CAN$(t,k,v)$, in a covering array for given values of the…
In this article we determine five previously unknown covering array numbers (CANs). We do so using properties of so called balanced covering arrays together with a computational result for these. The balance properties allow us to…
A covering array $t$-$CA(n,k,g)$, of size $n$, strength $t$, degree $k$, and order $g$, is a $k\times n$ array on $g$ symbols such that every $t\times n$ sub-array contains every $t\times 1$ column on $g$ symbols at least once. Covering…
A $t$-covering array with entries from the alphabet ${\cal Q}=\{0,1,\ldots,q-1\}$ is a $k\times n$ stack, so that for any choice of $t$ (typically non-consecutive) columns, each of the $q^{t}$ possible $t$-letter words over ${\cal Q}$…
The focus of this thesis is the study and construction of covering arrays, relying on maximal period sequences and other tools from finite fields. A covering array of strength $t$, denoted $\mathrm{CA}(N; t, k,v)$, is an $N\times k$ array…
Two vectors $x,y$ in $\mathbb{Z}_g^n$ are $ qualitatively$ $ independent$ if for all pairs $(a,b)\in \mathbb{Z}_g\times \mathbb{Z}_g$, there exists $i\in \{1,2,\ldots,n\}$ such that $(x_i,y_i)=(a,b)$. A covering array on a graph $G$,…
A sequence covering array, denoted \textsf{SCA}$(N;t,v)$, is a set of $N$ permutations of $\{0, \dots, v-1 \}$ such that each sequence of $t$ distinct elements of $\{0, \dots, v-1\}$ reads left to right in at least one permutation. The…
A (v,k,t) covering design, or covering, is a family of k-subsets, called blocks, chosen from a v-set, such that each t-subset is contained in at least one of the blocks. The number of blocks is the covering's size}, and the minimum size of…
An $(n,k)$ sequence covering array is a set of permutations of $[n]$ such that each sequence of $k$ distinct elements of $[n]$ is a subsequence of at least one of the permutations. An $(n,k)$ sequence covering array is perfect if there is a…
Modern software systems often consist of many different components, each with a number of options. Although unit tests may reveal faulty options for individual components, functionally correct components may interact in unforeseen ways to…
Given a weighted hypergraph $\mathcal{H}(V, \mathcal{E} \subseteq 2^V, w)$, the approximate $k$-cover problem seeks for a size-$k$ subset of $V$ that has the maximum weighted coverage by \emph{sampling only a few hyperedges} in…
Covering arrays are combinatorial objects that have been successfully applied in the design of test suites for testing systems such as software, circuits and networks, where failures can be caused by the interaction between their…
Capacitated Vertex Cover is the hard-capacitated variant of Vertex Cover: given a graph, a capacity for every vertex, and an integer $k$, the task is to select at most $k$ vertices that cover all edges and assign each edge to one of its…
A $(v,k,t)$ {\em covering design}, or {\em covering}, is a family of $k$-subsets, called blocks, chosen from a $v$-set, such that each $t$-subset is contained in at least one of the blocks. The number of blocks is the covering's {\em size},…
A $t-\a$ covering array is an $m\times n$ matrix, with entries from an alphabet of size $\alpha$, such that for any choice of $t$ rows, and any ordered string of $t$ letters of the alphabet, there exists a column such that the "values" of…