Abstract
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,..., e k , is defined as ∑ki = 1 w(e i )/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.
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Lin, RR., Kuo, WH. & Chao, KM. Finding a Length-Constrained Maximum-Density Path in a Tree. J Comb Optim 9, 147–156 (2005). https://doi.org/10.1007/s10878-005-6853-7
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DOI: https://doi.org/10.1007/s10878-005-6853-7