Note: Finding a length-constrained maximum-sum or maximum-density subtree and its application to logistics

Authors:
Hoong Chuin Lau;Trung Hieu Ngo;Bao Nguyen Nguyen
Affiliations:
Singapore Management University, Singapore 178902, Singapore;National University of Singapore, Singapore 119260, Singapore;National University of Singapore, Singapore 119260, Singapore
Venue:
Discrete Optimization
Year:
2006

Citing 6
Cited 6

An efficient algorithm for the length-constrained heaviest path problem on a tree

Information Processing Letters
Efficient algorithms for locating the length-constrained heaviest segments with applications to biomolecular sequence analysis

Journal of Computer and System Sciences - Computational biology 2002
Fast Algorithms for Finding Maximum-Density Segments of a Sequence with Applications to Bioinformatics

WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Linear-time algorithm for finding a maximum-density segment of a sequence

Information Processing Letters
An Optimal Algorithm for the Maximum-Density Segment Problem

SIAM Journal on Computing
Linear-time algorithms for computing maximum-density sequence segments with bioinformatics applications

Journal of Computer and System Sciences

Maximum segment sum is back: deriving algorithms for two segment problems with bounded lengths

PEPM '08 Proceedings of the 2008 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
An improved algorithm for finding a length-constrained maximum-density subtree in a tree

Information Processing Letters
An optimal algorithm for the maximum-density path in a tree

Information Processing Letters
The weight-constrained maximum-density subtree problem and related problems in trees

The Journal of Supercomputing
Calculational developments of new parallel algorithms for size-constrained maximum-sum segment problems

FLOPS'12 Proceedings of the 11th international conference on Functional and Logic Programming
The density maximization problem in graphs

Journal of Combinatorial Optimization

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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(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(nlog^2n) time for the generalized case when the edge lengths are positive real numbers, which indicates an improvement when U=@W(log^2n). 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.