Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Complexity of Scheduling Incompatible Jobs with Unit-Times
MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
Theoretical Computer Science - Game theory meets theoretical computer science
Reconfiguration of List Edge-Colorings in a Graph
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Finding Paths between graph colourings: PSPACE-completeness and superpolynomial distances
Theoretical Computer Science
The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies
SIAM Journal on Computing
On the complexity of reconfiguration problems
Theoretical Computer Science
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
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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.