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01798 am a22001933u 4500 |
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|a dc
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|a Ito, Takehiro
|e author
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|a Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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|a Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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|a Demaine, Erik D.
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|a Demaine, Erik D.
|e author
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|a Approximability of the Subset Sum Reconfiguration Problem
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|b Springer-Verlag,
|c 2014-04-07T16:53:30Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/86057
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|a 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.
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|a en_US
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|a Article
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|t Theory and Applications of Models of Computation
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