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We propose a graph-theoretic approach for the data path allocation problem. We decompose the problem into three subproblems: (1) register allocation. (2) operation assignment, and (3) connection allocation. The first two subproblems are modeled as two bipartite weighted matching problems and solved using the Hungarian Method [Pap82]. The third subproblem is solved using a greedy method. While previous researches suffer controversy over which one of subproblems (1) and (2) should be done fisk we show that, by taking the other into consideration while performing one, equally satisfactory results can be obtained. We have implemented two programs, LYRA and ARYL, to solve the subproblems in different orders, namely, "(l), (2). then (3)" and "(2), (l), then (3)", respectively. The matching paradigm allows us to take a more global approach toward the problem than previous researches do. For register allocation, our approach is the first one to guarantee minimal usage of registers while being able to take the interconnection cost into account For all the benchmarks from the literature, both LYRA and ARYL produced designs as good as, if not better than, those by others in very short time. This research has demonstrated that the bipartite weighted matching algorithm is indeed a very good solution for the data path allocation problem.