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The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies
, 2006
"... Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms,heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered ..."
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Cited by 14 (3 self)
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Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms,heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered
Journal of Combinatorial Optimization manuscript No. (will be inserted by the editor) Approximability of the Subset Sum Reconfiguration Problem
"... Abstract The subset sum problem is a wellknown NPcomplete 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 pap ..."
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Abstract The subset sum problem is a wellknown NPcomplete 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 NPhard, and is PSPACEcomplete 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 polynomialtime approximation scheme (PTAS), while the problem is APXhard if we are given a conflict graph. Keywords approximation algorithm · PTAS · reachability on solution space · subset sum 1