Optimal algorithms for tree partitioning
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Most uniform path partitioning and its use in image processing
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Journal of the ACM (JACM)
A Shifting Algorithm for Min-Max Tree Partitioning
Journal of the ACM (JACM)
A shifting algorithm for continuous tree partitioning
Theoretical Computer Science
A linear time algorithm for optimal tree sibling partitioning and approximation algorithms in Natix
VLDB '06 Proceedings of the 32nd international conference on Very large data bases
On the uniform edge-partition of a tree
Discrete Applied Mathematics
An algorithm for partitioning trees augmented with sibling edges
Information Processing Letters
New Upper Bounds on Continuous Tree Edge-Partition Problem
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Partitioning a Weighted Tree to Subtrees of Almost Uniform Size
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
A linear-time algorithm for finding an edge-partition with max-min ratio at most two
Discrete Applied Mathematics
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In this paper, we study how to partition a tree into edge-disjoint subtrees of approximately the same size. Given a tree T with n edges and a positive integer k@?n, we design an algorithm to partition T into k edge-disjoint subtrees such that the ratio of the maximum number to the minimum number of edges of the subtrees is at most two. The best previous upper bound of the ratio is three, given by Wu et al. [B.Y. Wu, H.-L. Wang, S.-T. Kuan, K.-M. Chao, On the uniform edge-partition of a tree, Discrete Applied Mathematics 155 (10) (2007) 1213-1223]. Wu et al. also showed that for some instances, it is impossible to achieve a ratio better than two. Therefore, there is a lower bound of two on the ratio. It follows that the ratio upper bound attained in this paper is already tight.