Interval-related problems on reconfigurable meshes

Abstract

Interval graphs provide a natural model for a vast number of scheduling and VLSI problems. A variety of interval graph problems have been solved on the PRAM family. Recently, a powerful architecture called the reconfigurable mesh has been proposed: in essence, a reconfigurable mesh consists of a mesh-connected architecture augmented by a dynamically reconfigurable bus system. It has been argued that the regular structure of the reconfigurable mesh is suitable for VLSI implementation. The authors develop a set of tools and show how they can be used to devise constant time algorithms to solve a number of interval-related problem on reconfigurable meshes. These problems include finding a maximum independent set, a minimum clique cover, a minimum dominating set, a minimum coloring, along with algorithms to compute the shortest path between a pair of intervals and, based on the shortest path, an algorithm to find the center of an interval graph. More precisely, with an arbitrary family of n intervals as input, all their algorithms run in constant time on a reconfigurable mesh of size n*n.<>