On the Algorithmic Aspects of Discrete and Lexicographic Helly-Type Theorems and the Discrete LP-Type Model

Helly's theorem says that, if every d+1 elements of a given finite set of convex objects in Rd have a common point, there is a point common to all of the objects in the set. In discrete Helly theorems the common point should belong to an a priori given set. In lexicographic Helly theorems the common point should not be lexicographically greater than a given point. Using discrete and lexicographic Helly theorems we get linear time solutions for various optimization problems. For this, we introduce the DLP-type (discrete linear programming

• Type: Journal
• Year: 2008
• Where: SIAMCOMP
• Authors: Nir Halman
• Keywords: Common Point, Lexicographic Helly, Linear Time, SIAMCOMP 2008