Stopping sets: Gamma-type results and hitting properties

Stopping sets: Gamma-type results and hitting properties

Independent sets and hitting sets of bicolored rectangular families

A bicolored rectangular family BRF is a collection of all axis-parallel rectangles contained in a given region Z of the plane formed by selecting a bottom-left corner from a set A and an upper-right corner from a set B. We prove that the maximum independent set and the minimum hitting set of a BRF have the same cardinality and devise polynomial time algorithms to compute both. As a direct conse...

Geometric Hitting Sets and Their Variants

Geometric Hitting Sets and Their Variants

L-Resilient Adversaries and Hitting Sets

The condition of t-resilience stipulates that an n-process program is only obliged to make progress when at least n− t processes are correct. Put another way, the live sets, the collection of process sets such that progress is required if all the processes in one of these sets are correct, are all sets with at least n − t processes. In this paper we study what happens when the live sets are any...

Hitting Sets Online and Unique-Max Coloring

We consider the problem of hitting sets online. The hypergraph (i.e., rangespace consisting of points and ranges) is known in advance, and the ranges to be stabbed are input one-by-one in an online fashion. The online algorithm must stab each range upon arrival. An online algorithm may add points to the hitting set but may not remove already chosen points. The goal is to use the smallest number...