Multiple Access Communications Using Combinatorial Designs

Colbourn, Charles J.

doi:10.1007/3-540-45878-6_1

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2006

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“…From the definition, it is clear that a t-design satisfies some strict properties of size, balance, and replication. This highly structured system provides optimal solutions to a variety of problems in computer science [6], like error-correcting codes [27,28], cryptography [23,25], and network interconnection [3,4], to mention a few. Special cases of t-designs include block designs, Steiner systems, triple and quadruple systems, projective geometries, affine geometries, and Hadamard designs.…”

Section: Introductionmentioning

confidence: 99%

Restricted b‐factors in bipartite graphs and t‐designs

Arámbula

Hicks

2006

J of Combinatorial Designs

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We present a new equivalence result between restricted b-factors in bipartite graphs and combinatorial t-designs. This result is useful in the construction of t-designs by polyhedral methods. We propose a novel linear integer programming formulation, which we call GDP, for the problem of finding t-designs that has a noteworthy advantage compared to the traditional set-covering formulation. We analyze some polyhedral properties of GPD, implement a branch-and-cut algorithm using it and solve several instances of small designs to compare with another point-block formulation found in the literature.

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