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Priority algorithms for the subset-sum problem

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  • Yuli Ye

    (University of Toronto)

  • Allan Borodin

    (University of Toronto)

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.

Suggested Citation

  • Yuli Ye & Allan Borodin, 2008. "Priority algorithms for the subset-sum problem," Journal of Combinatorial Optimization, Springer, vol. 16(3), pages 198-228, October.
    • Handle: RePEc:spr:jcomop:v:16:y:2008:i:3:d:10.1007_s10878-007-9126-9
    DOI: 10.1007/s10878-007-9126-9
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    References listed on IDEAS

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    1. J. Michael Moore, 1968. "An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs," Management Science, INFORMS, vol. 15(1), pages 102-109, September.
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