• The KIPS Transactions:PartA
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• v.13A no.6 s.103
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• pp.541-544
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• 2006

In a tree with each edge associated with a length and a weight (positive, negative, or zero are possible) we develop an O(nlognloglogn) time algorithm for finding a path such that its sum of weights is maximized and its sum of lengths does not exceed a given value. The previously best-known result is O($nlog^2n$), where n is the number of nodes in the tree.