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High-performance microprocessor families employ dynamic-thermal-management techniques to cope with the increasing thermal stress resulting from peaking power densities. These techniques operate on feedback generated from on-die thermal sensors. The allocation and the placement of thermal-sensing elements directly impact the effectiveness of the dynamic management mechanisms. In this paper, we propose systematic techniques for determining the optimal locations for thermal sensors to provide high-fidelity thermal monitoring of a complex microprocessor system. Our strategies can be divided into two main categories: uniform sensor allocation and nonuniform sensor allocation. In the uniform approach, the sensors are placed on a regular grid. The nonuniform allocation identifies an optimal physical location for each sensor such that the sensor's attraction toward steep thermal gradients is maximized, which can result in uneven concentrations of sensors on different locations of the chip. We also present a hybrid algorithm that shows the tradeoffs associated with number of sensors and expected accuracy. Our experimental results show that our uniform approach using interpolation can detect the chip temperature with a maximum error of 5.47degC and an average maximum error of 1.05degC . On the other hand, our nonuniform strategy is able to create a sensor distribution for a given microprocessor architecture, providing thermal measurements with a maximum error of 3.18degC and an average maximum error of 1.63degC across a wide set of applications.