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Power saving is an important issue when integrating the wireless LAN technology into mobile devices. Besides Quality of Service (QoS) guarantee, the IEEE 802.11e introduces an architecture called Scheduled Automatic Power-Save Delivery (S-APSD) aiming at delivering buffered frames to power save stations. In S-APSD, the Access Point (AP) schedules the Service Period (SP) of stations. To increase power efficiency, SPs should be scheduled to minimize the chance of overlapping. In a recent paper, an algorithm named Overlapping Aware S-APSD (OAS-APSD) was proposed to find the wake-up time schedule for a new Traffic Stream (TS) to minimize the chance of SP overlapping. The combination of OAS-APSD and HCF Controlled Channel Access (HCCA) was proved to outperform 802.11 Power Save Mode (PSM) with Enhanced Distributed Channel Access (EDCA) in power saving efficiency and QoS support. However, the OAS-APSD algorithm requires high online computational complexity which could make it infeasible for real systems. Without harming the optimality, this paper presents an efficient algorithm with much less complexity by exploiting the periodicity of service schedule. Because of largely reduced online computational complexity, the proposed algorithm is much more feasible than OAS-APSD.