Integer Problems on Reconfigurable Meshes, with Applications*

Problems with solutions based upon integer computations are collectively referred to as integer problems. Such problems occur routinely in pattern recognition, image processing, graph theory, and query processing. The purpose of this paper is to present constant time algorithms for computing the prefix sums of an integer sequence, and for solving the packing problem on reconfigurable meshes. These two algorithms are fundamental in the sense that they afford us efficient solutions to a wide variety of problems. Applications discussed in this paper include integer sorting, converting between the edge-list and the adjacency list representation of a graph, and converting between different representations of a rooted tree. All these problems are solved in constant time. As another application, we show how to compute the perimeter and the area of a binary image of size n ×n in O(loglogn ) time.