Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
(p-1)/(p+1)-approximate algorithms for p-traveling salemen problems on a tree with minmax objective
Discrete Applied Mathematics
A 5/4 linear time bin packing algorithm
Journal of Computer and System Sciences
A faster 2-approximation algorithm for the minmax p-traveling salesmen problem on a tree
Discrete Applied Mathematics
On the uniform edge-partition of a tree
Discrete Applied Mathematics
A linear time bin-packing algorithm
Operations Research Letters
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Minimum bounded edge-partition divides the edge set of a tree into the minimum number of disjoint connected components given a maximum weight for any component. It is an adaptation of the uniform edge-partition of a tree. An optimization algorithm is developed for this NP-hard problem, based on repeated bin packing of inter-related instances. The algorithm has linear running time for the class of 'balanced trees' common for the stochastic programming application which motivated investigation of this problem. Fast 2-approximation algorithms are formed for general instances by replacing the optimal bin packing with almost any bin packing heuristic. The asymptotic worst-case ratio of these approximation algorithms is never better than the absolute worst-case ratio of the bin packing heuristic used.