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A 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. One application of these objects is to generate software test suites to cover all t-sets of component interactions. Methods for construction of covering arrays for software testing have(More)
Given two graphs G and H, let f (G,H) denote the minimum integer n such that in every coloring of the edges of K n , there is either a copy of G with all edges having the same color or a copy of H with all edges having different colors. We show that f (G,H) is finite iff G is a star or H is acyclic. If S and T are trees with s and t edges, respectively, we(More)
Reliability is a major concern in the design of large disk arrays. Hellerstein et al. pioneered the study of erasure-resilient codes that allow one to reconstruct the original data even in the presence of disk failures. In this paper, we take a set systems view of the problem of constructing erasure-resilient codes. This leads to interesting extremal(More)
In this paper, we generalize the known topology-transparent medium access control protocols for mobile ad hoc networks by observing that their transmission schedule corresponds to an orthogonal array. Some new results on throughput are obtained as a consequence. We also show how to compute the probability of successful transmission if the actual node degree(More)
A (K 4 − e)-design on v + w points embeds a Steiner triple system if there is a subset of v points on which the graphs of the design induce the blocks of a Steiner triple system. It has been established that w ≥ v/3, and that when equality is met, such a minimum embedding of an STS(v) exists, except when v = 15. Equality only holds when v ≡ 15, 27 (mod 30).(More)
Let D be the triangle with an attached edge (i. e. D is the " kite " , a graph having vertices {a 0 , a 1 , a 2 , a 3 } and edges {a 0 , a 1 }, {a 0 , a 2 }, {a 1 , a 2 }, {a 0 , a 3 }). Bermond and Schönheim [6] proved that a kite-design of order n exists if and only if n ≡ 0 or 1 (mod 8). Let (W, C) be a nontrivial kite-design of order n ≥ 8, and let V ⊂(More)
Suppose m and t are integers such that 0 < t ≤ m. An (m, t) splitting system is a pair (X, B) where |X| = m, B is a set of m 2 subsets of X, called blocks such that for every Y ⊆ X and |Y | = t, there exists a block B ∈ B such that |B ∩ Y | = t 2 or |(X \ B) ∩ Y | = t 2. We will give some results on splitting systems for t = 2 or 4 which often depend on(More)