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- Myra B. Cohen, Charles J. Colbourn, Alan C. H. Ling
- Discrete Mathematics
- 2008

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)

- Myra B. Cohen, Charles J. Colbourn, Alan C. H. Ling
- ISSRE
- 2003

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 -sets of component… (More)

- Yeow Meng Chee, Charles J. Colbourn, Alan C. H. Ling
- Discrete Applied Mathematics
- 2000

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)

- Charles J. Colbourn, Torleiv Kløve, Alan C. H. Ling
- IEEE Transactions on Information Theory
- 2004

We develop a connection between permutation arrays that are used in powerline communication and well-studied combinatorial objects, mutually orthogonal latin squares (MOLS). From this connection, many new results on permutation arrays can be obtained.

- Charles J. Colbourn, Alan C. H. Ling
- Inf. Process. Lett.
- 2000

Maekawa considered a simple but suboptimal grid-based quorum generation scheme in which N sites in the network are logically organized in the form of a √ N ×√N grid, and the quorum sets are row–column pairs. Even though the quorum size 2 √ N of the grid scheme is twice as large as finite projective plane with optimal sized quorums, it has the advantage of… (More)

- Geoffrey Exoo, Alan C. H. Ling, John P. McSorley, Nicholas C. K. Phillips, Walter D. Wallis
- Discrete Mathematics
- 2002

A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, · · · , v+e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and… (More)

- Violet R. Syrotiuk, Charles J. Colbourn, Alan C. H. Ling
- DIALM-POMC
- 2003

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)

- Darryn E. Bryant, Heather Gavlas, Alan C. H. Ling
- Electr. J. Comb.
- 2003

Cyclic m-cycle systems of order v are constructed for all m ≥ 3, and all v ≡ 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for… (More)

- Alan C. H. Ling
- IEEE Trans. Information Theory
- 2002

- Charles J. Colbourn, Alan C. H. Ling, Gaetano Quattrocchi
- Discrete Mathematics
- 2005

Let D be the triangle with an attached edge (i. e. D is the “kite”, a graph having vertices {a0, a1, a2, a3} and edges {a0, a1}, {a0, a2}, {a1, a2}, {a0, a3}). 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 ⊂ W with |V | = v < n. A path… (More)