Approximability of the subset sum reconfiguration problem

Takehiro Ito, Erik D. Demaine

研究成果: Article査読

13 被引用数 (Scopus)


The subset sum problem is a well-known NP-complete problem in which we wish to find a packing (subset) of items (integers) into a knapsack with capacity so that the sum of the integers in the packing is at most the capacity of the knapsack and at least a given integer threshold. In this paper, we study the problem of reconfiguring one packing into another packing by moving only one item at a time, while at all times maintaining the feasibility of packings. First we show that this decision problem is strongly NP-hard, and is PSPACE-complete if we are given a conflict graph for the set of items in which each vertex corresponds to an item and each edge represents a pair of items that are not allowed to be packed together into the knapsack. We then study an optimization version of the problem: we wish to maximize the minimum sum among all packings in a reconfiguration. We show that this maximization problem admits a polynomial-time approximation scheme, while the problem is APX-hard if we are given a conflict graph.

ジャーナルJournal of Combinatorial Optimization
出版ステータスPublished - 2014 10月

ASJC Scopus subject areas

  • コンピュータ サイエンスの応用
  • 離散数学と組合せ数学
  • 制御と最適化
  • 計算理論と計算数学
  • 応用数学


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