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A constraint satisfaction problem (CSP) is a general framework that can formalize various application problems in artificial intelligence. In this paper, we focus on an important subclass of distributed partial CSP called the distributed maximal CSP that can be applied to more practical kinds of problems. Specifically, we propose a method of solving distributed maximal CSPs using a combination of approximate and exact algorithms that yields faster optimal solutions than otherwise possible using conventional methods. Experimental results are presented that demonstrate the effectiveness of the proposed new approach.