A Computational Paradigm on Network-Based Models of Computation

The maturation of computer science has strengthened the need to consolidate isolated algorithms and techniques into general computational paradigms. The main goal of this dissertation is to provide a unifying framework which captures the essence of a number of problems in seemingly unrelated contexts in database design, pattern recognition, image processing, VLSI design, computer vision, and robot navigation. The main contribution of this work is to provide a computational paradigm which involves the unifying framework, referred to as the multiple Query problem, along with a generic solution to the Multiple Query problem. To demonstrate the applicability of the paradigm, a number of problems from different areas of computer science are solved by formulating them in this framework. Also, to show practical relevance, two fundamental problems were implemented in the C language using MPI. The code can be ported onto many commercially available parallel computers; in particular, the code was tested on an IBM-SP2 and on a network of workstations

Optimal algorithms for the multiple query problem on reconfigurable meshes, with applications

The main contribution of this work is to show that a number of fundamental and seemingly unrelated problems in database design, pattern recognition, robotics, computational geometry, and image processing can be solved simply and elegantly by stating them as instances of a unifying algorithmic framework that we call the multiple query problem. The multiple query problem (MQ, for short) is a 5-tuple (Q, A, D, /spl phi/, /spl oplus/), where Q is a set of queries, A is a set of items, D is a set of solutions, /spl phi/: Q/spl times/A/spl rarr/D is a function, and /spl oplus/ is a commutative and associative binary operator over D. The input to the MQ problem consists of a sequence Q= of m queries from Q and of a sequence A= of n items from A. The goal is to compute, for every query q/sub i/ (1/spl les/i/spl les/m) its solution defined as /spl phi/(q/sub i/,A)=/spl phi/(q/sub i/,a/sub 1/)/spl oplus//spl phi/(q/sub i/,a/sub 2/)/spl oplus//spl middot//spl middot//spl middot//spl oplus//spl phi/(q/sub i/,a/sub n/). We begin by discussing a generic algorithm that solves a large class of MQ problems in O(/spl radic/m+f(n)) time on a reconfigurable mesh of size /spl radic/n/spl times//spl radic/n, where f(n) is the time necessary to compute the expression d/sub 1/ /spl oplus/ d/sub 2/ /spl oplus//spl middot//spl middot//spl middot//spl oplus/ d/sub n/ with d/sub i/ /spl isin/ D on such a platform. We then go on to show that the MQ framework affords us an optimal algorithm for the multiple point location problem on a reconfigurable mesh of size /spl radic/n/spl times//spl radic/n. Given a set A of n points and a set Q of m (m/spl les/n) points in the plane, our algorithm reports, in O(/spl radic/m+log log n) time, all points of Q that lie inside the convex hull of A. Quite surprisingly, our algorithm solves the multiple point location problem without computing the convex hull of A which, in itself, takes /spl Omega/(/spl radic/n) time on a reconfigurable mesh of size /spl radic/n/spl times//spl radic/n. Finally, we prove an /spl Omega/(/spl radic/m+g(n)) time lower bound for nontrivial MQ problems, where g(n) is the lower bound for evaluating the expression d/sub 1/ /spl oplus/ d/sub 2/ /spl oplus//spl middot//spl middot//spl middot//spl oplus/ d/sub n/ with d/sub i/ /spl isin/ D, on a reconfigurable mesh of size /spl radic/n/spl times//spl radic/n