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)
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)
The existence of modiied group divisible designs with block size four is settled with a handful of possible exceptions.
Component based software development is prone to unexpected interaction faults. The goal is to test as many potential interactions as is feasible within time and budget constraints. Two combinatorial objects, the orthogonal array and the covering array, can be used to generate test suites that provide a guarantee for coverage of all Ø-sets of component… (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)
Given n strings S1, S2, ..., Sn, and a pattern string P , the constrained multiple sequence alignment (CMSA) problem is to find an optimal multiple alignment of S1, S2,. .. , Sn such that the alignment contains P , i.e. in the alignment matrix there exists a sequence of columns each entirely composed of symbol P [k] for every k, where P [k] is the kth… (More)