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The resource allocation problem is a fundamental problem in distributed systems. In this paper, we focus on constructing nondominated (ND) local coteries to solve the problem. Distributed algorithms using coteries usually incur low communication overhead and have high degree of fault-tolerance, and ND coteries are candidates for the algorithms to achieve the highest degree of fault-tolerance. We define a new type of coteries, called p-coteries, to aid the construction of local coteries. We then develop theorems about the nondomination of p-coteries, and propose an operation, called pairwise-union (p-union), to help generate ND p-coteries from known ND coteries. ND p-coteries can then be used to generate ND local coteries for solving the distributed resource allocation problem.