SCALABLE AND OPTIMAL SPEED-UP PARALLEL ALGORITHMS FOR TEMPLATE MATCHING ON ARRAYS WITH RECONFIGURABLE OPTICAL BUSES

Abstract

The computational model on which the algorithms are developed is the array with reconfigurable optical buses (AROB). It integrates the advantages of both optical transmission and electronic computation. The main contributions of this paper are in designing several optimal and/or optimal speed-up template matching algorithms with varying degrees of parallelism on the AROB model. For an N × N digitized image and an M × M template, when the domains of the image and the template are O( log N)-bit integers, we first design several basic operations for window broadcasting and rotation. Then based on these basic operations, three efficient and scalable algorithms for template matching are derived using various numbers of processors on a two-dimensional (2-D) or 3-D AROB. For 1 ≤ r ≤ N, 1 ≤ p ≤ M ≤ q ≤ N, one runs in [Formula: see text] time using r × r processors, another runs in [Formula: see text], (resp. [Formula: see text]) time using pN × pN/ log M (resp. pN × pN × log N) processors, and the other runs in [Formula: see text] (resp. [Formula: see text]) time using pq × pq/ log M (or pq × pqN × log N) processors, respectively. The latter two algorithms can be tuned to run in O(1) time on a 2-D AROB. To the best of our knowledge, there are no algorithms which can reach this time complexity for this problem on a 2-D array architecture.