Further Improvements on Approximating the Uniform Cost-Distance Steiner Tree Problem

11/07/2022
by   Stephan Held, et al.
0

In this paper, we consider the Uniform Cost-Distance Steiner Tree Problem in metric spaces, a generalization of the well-known Steiner tree problem. Cost-distance Steiner trees minimize the sum of the total length and the weighted path lengths from a dedicated root to the other terminals, which have a weight to penalize the path length. They are applied when the tree is intended for signal transmission, e.g. in chip design or telecommunication networks, and the signal speed through the tree has to be considered besides the total length. Constant factor approximation algorithms for the uniform cost-distance Steiner tree problem have been known since the first mentioning of the problem by Meyerson, Munagala, and Plotkin. Recently, the approximation factor was improved from 2.87 to 2.39 by Khazraei and Held. We refine their approach further and reduce the approximation factor down to 2.15.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/05/2023

Tighter Approximation for the Uniform Cost-Distance Steiner Tree Problem

Uniform cost-distance Steiner trees minimize the sum of the total length...
research
11/01/2018

An O(n n) time Algorithm for computing the Path-length Distance between Trees

Tree comparison metrics have proven to be an invaluable aide in the reco...
research
10/06/2021

Fitting Distances by Tree Metrics Minimizing the Total Error within a Constant Factor

We consider the numerical taxonomy problem of fitting a positive distanc...
research
07/26/2019

Tight Approximation for Variants of Directed Steiner Tree via State-Tree Decomposition and Linear Programming Rounding

Directed Steiner Tree (DST) is a central problem in combinatorial optimi...
research
07/06/2023

Approximation Algorithms for Directed Weighted Spanners

In the pairwise weighted spanner problem, the input consists of an n-ver...
research
09/21/2022

Efficient inspection of underground galleries using k robots with limited energy

We study the problem of optimally inspecting an underground (underwater)...
research
01/19/2019

Approximation Algorithms for the A Priori TravelingRepairman

We consider the a priori traveling repairman problem, which is a stochas...

Please sign up or login with your details

Forgot password? Click here to reset