Equal Splits of Vertex-Weighted Trees

TL;DR

This paper presents a fast algorithm for partitioning vertex-weighted trees into two nearly equal parts by removing a single edge, or confirming such a partition is impossible.

Contribution

It introduces an efficient algorithm for finding an edge that splits a vertex-weighted tree into two equal-weight subtrees or proves none exists.

Findings

Algorithm efficiently finds the equal-split edge or confirms impossibility

Runs in polynomial time for large trees

Applicable to various weighted tree structures

Abstract

Given a tree of weighted vertices, it is sometimes possible to break the tree into two equally-weighted subtrees within an allowable error. We give a fast algorithm that finds an edge which breaks the tree into equal-weight components or determines there is no such edge.