Common intersection designs

Abstract

Motivated by an application to sensor networks, Lee and Stinson [6] defined a new type of set system termed a "common intersection design." Briefly, a mu-common intersection design is a I-design in which no pair of points occurs in more than one block, and in which any two disjoint blocks intersect at least mu blocks in common. In general, we want to maximize mu as a function of the other parmameters of the design. In this paper, we analyze combinatorial properties of common intersection designs. We determine necessary conditions for "optimal" common intersection designs and provide several existence results. Connections with other types of designs are pointed out. (C) 2005 Wiley Periodicals. Inc.