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IEEE 802.15.3c has recently been formed for developing a millimeter-wave (mmWave)-based alternative physical layer (PHY) for the existing 802.15.3 wireless personal area network (WPAN) standard, using the unlicensed 57-64 GHz band. However, the existing resource management schemes are inherently inefficient and insufficient for mmWave-based WPANs, without the consideration of the unique features of mm Wave communications: high Oxygen absorption rate and atmospheric attenuation, limited communication range, stringent power control for unlicensed usage, and the use of directional antennae. In this paper, by capturing the unique physical characteristics of mm Wave communications and based on the use of omni-or directional antennae, we derive the exclusive regions (ER) to allow efficient concurrent transmissions and develop an ER based scheduling algorithm to improve the network throughput of mm Wave based WPANs by several folds. Extensive simulations are conducted to demonstrate the effectiveness and efficiency of the proposed ER scheduling algorithm. The analysis and simulation results can provide important guidelines for future deployment of mm Wave based WPANs.