Algorithms of an optimal integer tree labeling
Data Structures and Algorithms
2013-05-27 v1 Populations and Evolution
Abstract
Suppose we label the vertices of a tree by positive integers. The weight of an edge is defined by a monotonically increasing function of the absolute value of the difference of the labels of its endpoints. We define the total cost of the labeling to be the sum of weight of all the edges.The problem we consider is that of determining for a given tree G and given a labeling of the leaves of G the minimum total cost labellings of G. In this paper we present an algorithm that works for any cost function satisfies the condition of monotony mentioned above. In a case of the function defined as the absolute value of the difference of the labels the fast algorithm is presented.
Cite
@article{arxiv.1305.5551,
title = {Algorithms of an optimal integer tree labeling},
author = {Alexander Bolshoy and Valery Kirzhner},
journal= {arXiv preprint arXiv:1305.5551},
year = {2013}
}