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 nodes in the tree and U is the length upper bound of the path. We present an algorithm that runs in O(nlog2n) time for the generalized case when the edge lengths are positive real numbers, which indicates an improvement when U=Ω(log2n). The complexity is reduced to O(nlogn) 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.
Network design, Algorithm, Computational complexity, Logistics
Numerical Analysis and Scientific Computing | Operations Research, Systems Engineering and Industrial Engineering
Intelligent Systems and Decision Analytics
LAU, Hoong Chuin; NGO, Trung Hieu; and Nguyen, Bao Nguyen.
Finding a length-constrained maximum-sum or maximum-density subtree and its application to logistics. (2006). Discrete Optimization. 3, (4), 385-391. Research Collection School Of Information Systems.
Available at: http://ink.library.smu.edu.sg/sis_research/1188
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.