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

Let T = (V, E, w) be an 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 e1, e2, . . . , ek, is defined as k i=1 w(ei )/k. The length of a path is the number of its edges. Given a tree with n edges and a lower bound L where 1 ≤ L ≤ n, 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.

• Type: Conference
• Year: 2003
• Where: ISAAC
• Authors: Rung-Ren Lin, Wen-Hsiung Kuo, Kun-Mao Chao
• Keywords: Edge Set E, Edge Weight Function, ISAAC 2003, Weighted Tree