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)
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)
A Kirkman school project design on v elements consists of the maximum admissible number of disjoint parallel classes, each containing blocks of sizes three except possibly one of size two or four. Cern y, Horr ak, and Wallis completely settled existence when v 0; 2 (mod 3) and made some progress and advanced a conjecture when v 1 (mod 3). In this paper, a… (More)
The existence of modiied group divisible designs with block size four is settled with a handful of possible exceptions.