Approximability of the Subset Sum Reconfiguration Problem
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Author(s)
Ito, Takehiro
Demaine, Erik D.
Date Issued
May 2011
Journal
Theory and Applications of Models of Computation
Publisher
Springer-Verlag
Citation
Ito, Takehiro, and Erik D. Demaine. “Approximability of the Subset Sum Reconfiguration Problem.” Lecture Notes in Computer Science (2011): 58–69.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1007/978-3-642-20877-5_7
