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This paper proposes task-scheduling algorithms designed to save energy in ad hoc networks by using a novel concept of "affinity" as the scheduling metric. This notion of affinity is used to represent the task-linking topology. For one-hop ad hoc networks, we define three types of affinity measures: node affinity, task affinity, and weighted affinity. Node affinity is defined as the weighted sum of incoming and outgoing task flows at each node, and task affinity as the sum of node affinities of source and destination nodes for each task. Based on these affinity measures, we consider three heuristic scheduling algorithms that are executable in real time: 1) affinity-first shortest task scheduling Qat; 2) task-size-first affinity-based scheduling Qta; and 3) task-size weighted-affinity scheduling Qwa. These algorithms have the advantage of making the total duration of the doze state of all the nodes in the network longer than in other conventional schemes, thereby achieving significant power saving (PS). Our simulation experiments suggest that the PS performance of Qwa is comparable to optimal scheduling (which is not implementable in practice for realistic link topologies). We also present a framework for a PS medium-access-control (MAC) protocol in which our scheduling algorithm can be deployed, and we describe how to enhance the existing 802.11 PS MAC to implement our framework. Simulation results demonstrate that our enhanced PS MAC protocol combined with affinity-based scheduling improves power efficiency and throughput significantly over other existing schemes. [ABSTRACT FROM AUTHOR]