The discrete relaxation algorithm (DRA) is a computational technique that enforces arc consistency (AC) in a constraint satisfaction problem (CSP). The original sequential AC-1 algorithm suffers from O (n/sup 3/m/sup 3/) time complexity, and even the optimal sequential AC-4 algorithm is O (n/sup 2/m/sup 2/) for an n-object and m-label DRA problem. Sample problem runs show that these algorithms are all too slow to meet the need for any useful, real-time CSP applications. A parallel DRA5 algorithm that reaches a lower bound of O (nm)(where the number of processors is polynomial in the problem size) is given. A fine-grained, massively parallel hardware computer architecture has been designed for the DRA5 algorithm. For practical problems, many orders of magnitude of efficiency improvement can be reached on such a hardware architecture.