Approximability of the subset sum reconfiguration problem

Takehiro Ito, Erik D. Demaine

研究成果: Conference contribution

11 被引用数 (Scopus)

抄録

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 the reconfiguration. We show that this maximization problem admits a polynomial-time approximation scheme (PTAS), while the problem is APX-hard if we are given a conflict graph.

本文言語English
ホスト出版物のタイトルTheory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings
ページ58-69
ページ数12
DOI
出版ステータスPublished - 2011
イベント8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011 - Tokyo, Japan
継続期間: 2011 5 232011 5 25

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
6648 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Conference

Conference8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011
国/地域Japan
CityTokyo
Period11/5/2311/5/25

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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