Algorithm for the Length-Constrained Maximum-Density Path Problem in a Tree with Uniform Edge Lengths
نویسنده
چکیده
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 algorithms run in O(nL) or O(n log n) time.
منابع مشابه
Linear-Time Algorithm for the Length-Constrained Heaviest Path Problem in a Tree with Uniform Edge Lengths∗
Given a tree T with edge lengths and edge weights, and a value B, the length-constrained heaviest path problem is to find a path in T with maximum path weight whose path length is at most B. We present a linear time algorithm for the problem when the edge lengths are uniform, i.e., all one. This algorithm with slight modification can be used to find the heaviest path of length exactly B in T in...
متن کاملLinear-Time Algorithm for the Length-Constrained Heaviest Path Problem in a Tree with Uniform Edge Lengths
Given a tree T with edge lengths and edge weights, and a value B, the length-constrained heaviest path problem is to find a path in T with maximum path weight whose path length is at most B. We present a linear time algorithm for the problem when the edge lengths are uniform, i.e., all one. This algorithm with slight modification can be used to find the heaviest path of length exactly B in T in...
متن کاملFinding a length-constrained maximum-sum or maximum-density subtree and its application to logistics
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...
متن کاملAn improved algorithm for finding a length-constrained maximum-density subtree in a tree
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 کاملOptimal Algorithms for Finding Density-Constrained Longest and Heaviest Paths in a Tree
Let T be a tree with n nodes, in which each edge is associated with a length and a weight. The density-constrained longest (heaviest) path problem is to find a path of T with maximum path length (weight) whose path density is bounded by an upper bound and a lower bound. The path density is the path weight divided by the path length. We show that both problems can be solved in optimal O(n logn) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IEICE Transactions
دوره 98-D شماره
صفحات -
تاریخ انتشار 2015