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In this paper, the routing problem for two-dimensional (2-D) field programmable gate arrays of a Xilinx-like architecture is studied. We first propose an efficient one-step router that makes use of the main characteristics of the architecture. Then we propose an improved approach of coupling two greedy heuristics designed to avoid an undesired decaying effect, a dramatically degenerated router performance on the near completion stages. This phenomenon is commonly observed on results produced by the conventional deterministic routing strategies using a single optimization cost function. Consequently, our results are significantly improved on both the number of routing tracks and routing segments by just applying low-complexity algorithms. On the tested MCNC and industrial benchmarks, the total number of tracks used by the best known two-step global/detailed router is 28% more than that used by our proposed method.