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Energy-efficient scheduling of sequential tasks with precedence constraints on multiprocessor computers with dynamically variable voltage and speed is investigated as combinatorial optimization problems. In particular, the problem of minimizing schedule length with energy consumption constraint and the problem of minimizing energy consumption with schedule length constraint are considered. Our scheduling problems contain three nontrivial sub problems, namely, precedence constraining, task scheduling, and power supplying. Each sub problem should be solved efficiently so that heuristic algorithms with overall good performance can be developed. Such decomposition of our optimization problems into three sub problems makes design and analysis of heuristic algorithms tractable. Three types of heuristic power allocation and scheduling algorithms are proposed for precedence constrained sequential tasks with energy and time constraints, namely, pre-power-determination algorithms, post-power-determination algorithms, and hybrid algorithms. The performance of our algorithms are analyzed and compared with optimal schedules analytically. Such analysis has not been conducted in the literature for any algorithm. Therefore, our investigation in this paper makes initial contribution to analytical performance study of heuristic power allocation and scheduling algorithms for precedence constrained sequential tasks. Our extensive simulation data demonstrate that for wide task graphs, the performance ratios of all our heuristic algorithms approach one as the number of tasks increases.