A distributed formation of orthogonal convex polygons in mesh-connected multicomputer

Abstract

The rectangular faulty block model is the most commonly used fault model in designing a fault-tolerant and deadlock-free routing algorithm in mesh-connected multicomputers. The convexity of a rectangle facilitates simple and efficient ways to route messages around fault regions using relatively few virtual channels to avoid deadlock. However, such a faulty block may include many nonfaulty nodes which are disabled, i.e. they are not involved in the routing process. Therefore, it is important to define a fault region that is convex, and at the same time, to include a minimum number of nonfaulty nodes. In this paper we propose a simple and efficient distributed algorithm that can quickly construct a set of special convex polygons, called orthogonal convex polygons, from a given set of rectangular faulty blocks in a 2-D mesh (or 2-D torus). The formation of orthogonal convex polygons is done through a labeling scheme based on iterative message exchanges among neighboring nodes.