A Parallel Architecture for Discrete Relaxation Algorithm

Discrete relaxation techniques have proven useful in solving a wide range of problems in digital signal and digital image processing, artificial intelligence, operations research, and machine vision. Much work has been devoted to finding efficient hardware architectures. This paper shows that a conventional hardware design for a Discrete Relaxation Algorithm (DRA) suffers from O(n2m3) time complexity and O(n2m2) space complexity. By reformulating DRA into a parallel computational tree and using a multiple tree-root pipelining scheme, time complexity is reduced to O(nm), while the space complexity is reduced by a factor of 2. For certain relaxation processing, the space complexity can even be decreased to O(nm). Furthermore, a technique for dynamic configuring an architectural wavefront is used which leads to an O(n) time highly concurrent DRA3 architecture.