Linear-Time Algorithm for the Length-Constrained Heaviest Path Problem in a Tree with Uniform Edge Lengths

Abstract

Given a tree T with edge lengths and edge weights, and a value B, the length-constrained heaviest path problem is to find a path in T with maximum path weight whose path length is at most B. We present a linear time algorithm for the problem when the edge lengths are uniform, i.e., all one. This algorithm with slight modification can be used to find the heaviest path of length exactly B in T in linear time.