An Efficient Algorithm for Node-Weighted Tree Partitioning with Subtrees' Weights in a Given Range

Abstract

SUMMARYTree partitioning arises in many parallel and distributed computing applications and storage systems. Some operator scheduling problems need to partition a tree into a number of vertex-disjoint subtrees such that some constraints are satisfied and some criteria are optimized. Given a tree T with each vertex or node assigned a nonnegative integer weight, two nonnegative integers l and u (l < u), and a positive integer p, we consider the following tree partitioning problems: partitioning T into minimum number of subtrees or p subtrees, with the condition that the sum of node weights in each subtree is at most u and at least l. To solve the two problems, we provide a fast polynomial-time algorithm, including a preprocessing method and another bottom-up scheme with dynamic programming. With experimental studies, we show that our algorithm outperforms another prior algorithm presented by Ito et al. greatly.

Partitioning algorithms for weighted trees and cactus graphs

“…Furthermore, Ito et al proved that one can decide these problems on trees in polynomial time -in particular they gave O(n 5 ) and O(p 4 n) algorithms [8]. Luo et al added a preprocessing procedure and showed that their method outperforms the one given by Ito et al in regard to computational time [13].…”