Priority algorithms for the subset-sum problem

Abstract

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 Subset-Sum 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.