Finding a Length-Constrained Maximum-Density Path in a Tree
نویسندگان
چکیده
منابع مشابه
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-den...
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Given a tree T with weight and length on each edge, as well as a lower bound L and an upper bound U , the so-called length-constrained maximum-density subtree problem is to find a maximum-density subtree in T such that the length of this subtree is between L and U . In this study, we present an algorithm that runs in O(nU log n) time for the case when the edge lengths are positive integers, whe...
متن کاملFinding a maximum-density path in a tree under the weight and length constraints
Let T = (V ,E) be a tree with n nodes such that each node v is associated with a value-weight pair (valv,wv), where the value valv is a real number and the weight wv is a positive integer. The density of a path P = 〈v1, v2, . . . , vk〉 is defined as ∑k i=1 vali/ ∑k i=1 wi . The weight of P , denoted by w(P ), is ∑k i=1 wi . Given a tree of n nodes, two integers wmin and wmax, and a length lower...
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SUMMARY Given an edge-weighted tree with n vertices and a positive integer L, the length-constrained maximum-density path problem is to find a path of length at least L with maximum density in the tree. The density of a path is the sum of the weights of the edges in the path divided by the number of edges in the path. We present an O(n) time algorithm for the problem. The previously known algor...
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We study the problem of finding a length-constrained maximum-density path in a tree with weight and length on each edge. This problem was proposed in [R.R. Lin, W.H. Kuo, K.M. Chao, Finding a length-constrained maximum-density path in a tree, Journal of Combinatorial Optimization 9 (2005) 147–156] and solved in O(nU ) time when the edge lengths are positive integers, where n is the number of no...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2005
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-005-6853-7