Finding a Length-Constrained Maximum-Density Path in a Tree

Let T = (V,E,w) be a rooted, undirected, and weighted tree with node set V and edge set E, where w(e) is an edge weight function for e∈E. The density of a path, say e 1, e 2, ..., e k , is defined as \(\sum^k_{i=1}w(e_i)\)/k. Given a tree with n edges, this paper presents two efficient algorithms for finding a maximum-density path of length at least L in O(nL) time. One of them is further modified to solve some special cases such as full m-ary trees in O(n) time.

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