Greedy algorithms are simple, but their relative power is not well understood. The priority framework [5] captures a key notion of "greediness" in the sense that it processes (in some locally optimal manner) one data item at a time, depending on and only on the current knowledge of the input. This algorithmic model provides a tool to assess the computational power and limitations of greedy algorithms, especially in terms of their approximability. In this paper, we study priority algorithm approximation ratios for the Subset-Sum Problem, focusing on the power of revocable decisions. We first provide a tight bound of α ≈ 0.657 for irrevocable priority algorithms. We then show that the approximation ratio of fixed order revocable priority algorithms is between β ≈ 0.780 and γ ≈ 0.852, and the ratio of adaptive order revocable priority algorithms is between 0.8 and δ β 0.893.
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