Abstract
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 ( n U ) time when the edge lengths are positive integers, where n is the number of nodes in the tree and U is the length upper bound of the path. We present an algorithm that runs in O ( n log 2 n ) time for the generalized case when the edge lengths are positive real numbers, which indicates an improvement when U = Ω ( log 2 n ) . The complexity is reduced to O ( n log n ) when edge lengths are uniform. In addition, we study the generalized problems of finding a length-constrained maximum-sum or maximum-density subtree in a given tree or graph, providing algorithmic and complexity results.
Published Version
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