Applications of combinatorial designs in computer science

Abstract

The theory of combinatorial designs has been used in widely different areas of computation concerned with the design and analysis of both algorithms and hardware. Combinatorial designs capture a subtle balancing property that is inherent in many difficult problems and hence can provide a sophisticated tool for addressing these problems. The role of combinatorial designs in solving many problems that are basic to the field of computing is explored in this paper. Case studies of many applications of designs to computation are given; these constitute a first survey, which provides a representative sample of uses of designs. More importantly, they suggest paradigms in which designs can be used profitably in algorithm design and analysis.

Replica Placement for Availability in the Worst Case

“…To our knowledge, we are the first to explore the use of t-packings for replica placement in distributed systems. That said, such block designs have found application in several diverse domains, as surveyed elsewhere (e.g., [11], [9], [33]). The most conceptually related use of block designs to ours is their use in constructing quorum systems (e.g., [29]).…”

Computational complexity of reconstruction and isomorphism testing for designs and line graphs

“…Combinatorial design theory is a rich subject on the interface of several disciplines, including coding and information theory, cryptography, combinatorics, group theory, and geometry. In particular, the study of designs with high symmetry properties has a very long history and establishes deep connections between these areas (see, e.g., [12,15,[20][21][22][23]30]). …”

Combinatorial Designs (W. D. Wallis)

“…The consideration of almost periodic coefficients is a recurring theme. The authors note that they were heavily influenced in this direction by the papers of Moore [1] and Markus and Moore [2].…”

“…His choice of student is interesting, as we wonder if a computer science student would be interested in the construction of combinatorial designs. A recent paper [2] begins, "The theory of combinatorial designs has been used in widely different areas of computation, in the design and analysis of both algorithms and hardware," thus indicating that the interest is there.…”