Approximability of the subset sum reconfiguration problem

Takehiro Ito, Erik D. Demaine

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (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 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.

Original languageEnglish
Title of host publicationTheory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings
Number of pages12
Publication statusPublished - 2011
Event8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011 - Tokyo, Japan
Duration: 2011 May 232011 May 25

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6648 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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