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.

A note 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. (Proofs for k = 3 and k = 4 are omitted here.) 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

A note on the uniform edge-partition of a tree 1

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. (Proofs for k = 3 and k = 4 are omitted here.) 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