Common Transversals for Families of Sets†

Disjoint Common Partial Transversals of Two Families of Sets

Common Transversals

Given t families, each family consisting of s finite sets, we show that if the families “separate points" in a natural way, and if the union of all the sets in all the families contains more than (s+1)t st 1 1 elements, then a common transversal of the t families exists. In case each family is a covering family, the bound is st st 1. Both of these bounds are best possible. This work extends rec...

Efficient Algorithms for Common Transversals

Suppose we are gIven a set S of n (possibly intersecting) simple objects in the plane, such that for every pair of objects in S, the intersection of the boundaries of these two objects has at most a connected components. The integer a is independent of n, Le. a.=O (1). \Ve consider the problem of detennining whether there exists a straight line that goes through every object in S. We give an 0 ...

Computing shortest transversals of sets

Given a family of objecte in the plane, the line transversal problem is to compute a line that intersects every member of the family. In this paper we examine a variation of the line transversal problem that involves computing a shortest line segment that intersects every member of the family. In particular, we give O(nlogn) time algorithms for computing a shortest transversal of a family of n ...

Geometric Permutations and Common Transversals