Bin packing with divisible item sizes
Journal of Complexity
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
On the equal-subset-sum problem
Information Processing Letters
Integer knapsack and flow covers with divisible coefficients: polyhedra, optimization and separation
Discrete Applied Mathematics
Introduction to algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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We study a motion planning problem where items have to be transported from the top room of a tower to the bottom of the tower, while simultaneously other items have to be transported in the opposite direction. Item sets are moved in two baskets hanging on a rope and pulley. To guarantee stability of the system, the weight difference between the contents of the two baskets must always stay below a given threshold.We prove that it is $\varPi_{2}^{p}$-complete to decide whether some given initial situation of the underlying discrete system can lead to a given goal situation. Furthermore we identify several polynomially solvable special cases of this reachability problem, and we also settle the computational complexity of a number of related questions.