Spanning trees with minimum weighted degrees

Authors:
Mohammad Ghodsi;Hamid Mahini;Kian Mirjalali;Shayan Oveis Gharan;Amin S. Sayedi R.;Morteza Zadimoghaddam
Affiliations:
Department of Computer Engineering, Sharif University of Technology, Tehran, Iran and School of Computer Science, Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran and School of Computer Science, Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran
Venue:
Information Processing Letters
Year:
2007

Citing 9
Cited 2

Approximating the minimum degree spanning tree to within one from the optimal degree

SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Many birds with one stone: multi-objective approximation algorithms

STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The complexity of restricted spanning tree problems

Journal of the ACM (JACM)
A matter of degree: improved approximation algorithms for degree-bounded minimum spanning trees

STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Steiner Trees and Beyond: Approximation Algorithms for Network Design

Steiner Trees and Beyond: Approximation Algorithms for Network Design
Approximation algorithms for finding low-degree subgraphs

Networks
Minimum Bounded Degree Spanning Trees

FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Delegate and conquer: an LP-based approximation algorithm for minimum degree MSTs

ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
A push-relabel algorithm for approximating degree bounded MSTs

ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I

Network Design with Weighted Degree Constraints

WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Network design with weighted degree constraints

Discrete Optimization

Quantified Score

Hi-index	0.89

Visualization

Abstract

Given a metric graph G, we are concerned with finding a spanning tree of G where the maximum weighted degree of its vertices is minimum. In a metric graph (or its spanning tree), the weighted degree of a vertex is defined as the sum of the weights of its incident edges. In this paper, we propose a 4.5-approximation algorithm for this problem. We also prove it is NP-hard to approximate this problem within a 2-ε factor.