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A major problem in wireless networks is coping with limited resources, such as bandwidth and energy. These issues become a major algorithmic challenge in view of the dynamic nature of the wireless domain. We consider in this paper the single-transmitter power assignment problem under time-varying channels, with the objective of maximizing the data throughput. It is assumed that the transmitter has a limited power budget, to be sequentially divided during the lifetime of the battery. We deviate from the classic work in this area, which leads to explicit “water-filling” solutions, by considering a realistic scenario where the channel state quality changes arbitrarily from one transmission to the other. The problem is accordingly tackled within the framework of competitive analysis, which allows for worst-case performance guarantees in setups with arbitrarily varying channel conditions. We address both a “discrete” case, where the transmitter can transmit only at a fixed power level, and a “continuous” case, where the transmitter can choose any power level out of a bounded interval. For both cases, we propose online power-allocation algorithms with proven worst-case performance bounds. In addition, we establish lower bounds on the worst-case performance of any online algorithm and show that our proposed algorithms are optimal.