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Beacon period (BP) is an overhead in UWB MBOA MAC, since no data frame is allowed during a BP. In this letter, we model the current BP contraction scheme in MBOA spec as a greedy distance-2 graph coloring algorithm, and formulate the BP contraction problem as a 0-1 programming problem. The theoretical numerical results show that the current BP contraction algorithm has good performance. Furthermore, we study the impact of device joining/leaving order on the performance of the algorithm. Simulation results demonstrate that the impact is not significant and the performance of the algorithm is stable with varied device ordering. Therefore, we conclude that there is no much room for any further significant improvement over the current BP contraction algorithm in MBOA spec.