A note on the minimum bounded edge-partition of a tree

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.