Priority Algorithms for the Subset-Sum Problem

Greedy algorithms are simple, but their relative power is not well understood. The priority framework (Borodin et al. in Algorithmica 37:295–326, 2003) 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 SubsetSum Problem, focusing on the power of revocable decisions, for which the accepted data items can be later rejected to maintain the feasibility of the solution. 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 ≈ 0.893.