On the uniform edge-partition of a tree

We study the problem of uniformly partitioning the edge set of a tree with n edges into k connected components, where k ≤ n. The objective is to minimize the ratio of the maximum to the minimum number of edges of the subgraphs in the partition. We show that, for any tree and k ≤ 4, there exists a k-split with ratio at most two. For general k, we propose a simple algorithm that finds a k-split with ratio at most three in O(n log k) time. Experimental results on random trees are also shown. Key words: tree, partition, optimization problem, algorithm.

• Type: Journal
• Year: 2007
• Where: DAM
• Authors: Bang Ye Wu, Hung-Lung Wang, Shih Ta Kuan, Kun-Mao Chao
• Keywords: DAM 2007, Minimum Number, Simple Algorithm, Tree