Interval Graph Problems on Reconfigurable Meshes

A graph G is an interval graph if there is a one-one correspondence between its vertices and a family I of intervals, such that two vertices in G are adjacent if and only if their corresponding intervals overlap. In this context, the family I of intervals is referred to as an interval model of G. Recently, a powerful architecture called the reconngurable mesh has been proposed: in essence, a reconngurable mesh consists of a mesh-connected architecture augmented by a dynamically reconngurable bus system. In this paper, we exploit the reconngurable mesh architecture for the purpose of obtaining constant-time algorithms for a number of computational problems on interval graphs. These problems include nding a maximum size clique, a maximum weight clique in the presence of integer weights, a maximum size independent set, a minimum clique cover, a minimum size dominating set, a shortest path between any two vertices in G, the diameter and the center of G, as well as Breadth-First Search and Depth-First Search trees for G. Speciically, with an n-vertex interval graph speciied by its interval model as input, all our algorithms run in constant time on a reconngurable mesh of size n n.