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Distributed Algorithms for Minimum Degree Spanning Trees [article]

Michael Dinitz and Magnús M. Halldórsson and Calvin Newport
2018 arXiv   pre-print
The minimum degree spanning tree (MDST) problem requires the construction of a spanning tree T for graph G=(V,E) with n vertices, such that the maximum degree d of T is the smallest among all spanning  ...  Our first result is a randomized distributed algorithm that constructs a spanning tree of maximum degree d̂ = O(dn).  ...  Introduction & Related Work We present two new distributed approximation algorithms for the minimum degree spanning tree (MDST) problem, which requires the construction of a spanning tree T for graph G  ... 
arXiv:1806.03365v1 fatcat:mnoho7zkevfv5ndztigcbwo7je

A distributed approximation algorithm for the minimum degree minimum weight spanning trees [article]

Christian Lavault
2006 arXiv   pre-print
Fischer has shown how to compute a minimum weight spanning tree of degree at most b Δ^* + _b n in time O(n^4 + 1/ b) for any constant b > 1, where Δ^* is the value of an optimal solution and n is the number  ...  In this paper, we propose a distributed version of Fischer's algorithm that requires messages and time complexity O(n^2 + 1/ b), and O(n) space per node.  ...  To our knowledge, this is the first distributed approximation algorithm for the minimum degree minimum weight spanning tree problem.  ... 
arXiv:cs/0607031v1 fatcat:vtrsyxdl7za4fjg4wmni4j6cmi

A distributed approximation algorithm for the minimum degree minimum weight spanning trees

Christian Lavault, Mario Valencia-Pabon
2008 Journal of Parallel and Distributed Computing  
Fischer [3] has shown how to compute a minimum weight spanning tree of degree at most b∆ * + ⌈log b n⌉ in time O(n 4+1/ln b ) for any constant b > 1, where ∆ * is the value of an optimal solution and n  ...  In this paper, we propose a distributed version of Fischer's algorithm that requires messages and time complexity O(n 2+1/ln b ), and O(n) space per node.  ...  To our knowledge, this is the first distributed approximation algorithm for the minimum degree minimum weight spanning tree problem.  ... 
doi:10.1016/j.jpdc.2007.07.005 fatcat:nrzhl3nwoze4hmh2oillzyr5hy

Self-stabilizing minimum degree spanning tree within one from the optimal degree

Lélia Blin, Maria Gradinariu Potop-Butucaru, Stephane Rovedakis
2011 Journal of Parallel and Distributed Computing  
We propose a self-stabilizing algorithm for constructing a Minimum-Degree Spanning Tree (MDST) in undirected networks.  ...  maximum degree of a spanning tree of the network.  ...  Minimum Degree Spanning Tree (MDST) A legitimate configuration for the MDST is a configuration that outputs an unique spanning tree of minimum degree.  ... 
doi:10.1016/j.jpdc.2010.08.019 fatcat:tspkrmzflfgfvje4rrxjuflrna

Self-stabilizing minimum-degree spanning tree within one from the optimal degree

Lelia Blin, Maria Gradinariu Potop-Butucaru, Stephane Rovedakis
2009 2009 IEEE International Symposium on Parallel & Distributed Processing  
We propose a self-stabilizing algorithm for constructing a Minimum-Degree Spanning Tree (MDST) in undirected networks.  ...  maximum degree of a spanning tree of the network.  ...  Minimum Degree Spanning Tree (MDST) A legitimate configuration for the MDST is a configuration that outputs an unique spanning tree of minimum degree.  ... 
doi:10.1109/ipdps.2009.5161042 dblp:conf/ipps/BlinPR09 fatcat:rkazjvg5nbb65pcogmn3jp4zwi

THE FIRST APPROXIMATED DISTRIBUTED ALGORITHM FOR THE MINIMUM DEGREE SPANNING TREE PROBLEM ON GENERAL GRAPHS

LÉLIA BLIN, FRANCK BUTELLE
2004 International Journal of Foundations of Computer Science  
In this paper we present the first distributed algorithm on general graphs for the Minimum Degree Spanning Tree problem. The problem is NP-hard in sequential.  ...  Our algorithm give a Spanning Tree of a degree at most 1 from the optimal.  ...  Introduction In this paper we focus on the problem of finding a distributed approximated algorithm for a Minimum Degree Spanning Tree (MDegST).  ... 
doi:10.1142/s0129054104002571 fatcat:hbuqxxql55c7vd5nudxr3j4zea

Self-stabilizing minimum-degree spanning tree within one from the optimal degree Self-stabilizing minimum-degree spanning tree within one from the optimal degree

Lélia Blin, Maria Gradinariu Potop-Butucaru, Stephane Rovedakis, Lélia Blin, Maria Gradinariu Potop-Butucaru, Stephane Rovedakis, Lélia Blin, Maria Potop-Butucaru, Stéphane Rovedakis
2009 IEEE International Symposium on Parallel&Distributed Processing   unpublished
We propose a self-stabilizing algorithm for constructing a Minimum-Degree Spanning Tree (MDST) in undirected networks.  ...  maximum degree of a spanning tree of the network.  ...  Minimum Degree Spanning Tree (MDST) A legitimate configuration for the MDST is a configuration that outputs an unique spanning tree of minimum degree.  ... 
fatcat:ucxn4sffubg5rbzk6l2pgntbfy

The first approximated distributed algorithm for the minimum degree spanning tree problem on general graphs

L. Blin, F. Butelle
Proceedings International Parallel and Distributed Processing Symposium  
In this paper we present the first distributed algorithm on general graphs for the Minimum Degree Spanning Tree problem. The problem is NP-hard in sequential.  ...  Our algorithm give a Spanning Tree of a degree at most 1 from the optimal.  ...  Introduction In this paper we focus on the problem of finding a distributed approximated algorithm for a Minimum Degree Spanning Tree (MDegST).  ... 
doi:10.1109/ipdps.2003.1213299 dblp:conf/ipps/BlinB03 fatcat:4ejuu4shcve7nlpdt2jjsms5ya

Scale-Free spanning trees of complex networks

Kim Dong-Hee, Jeong Hawoong
2004 Journal of the Korean Physical Society  
Minimum Spanning Tree (III): degree The degree distribution follows power-law ! 1. At each step one of remaining edges is randomly chosen for removal. 2.  ...  Select only one edge with equal probability.Burning (II) : degree distribution scale-free spanning trees !  ...  Conclusions We investigate the degree distribution of the spanning trees of complex networks.  ... 
doi:10.3938/jkps.44.624 fatcat:w44lfhjee5fn5gbivzvip2xxve

Underlying Scale-Free Trees in Complex Networks

D.-H. Kim, S.-W. Son, Y.-Y. Ahn, P.-J. Kim, Y.-H. Eom, H. Jeong
2005 Progress of Theoretical Physics Supplement  
We also find that the degree distribution of spanning trees shows scale-free behavior for many model and real-world networks and the degree of the spanning trees has strong correlation with their original  ...  Interestingly, these two minimum spanning trees from different methods not only have same scale-free behavior but overlap each other in their structures.  ...  We measure the degree distribution of each spanning tree and compare the degree of the spanning tree with that from its original network.  ... 
doi:10.1143/ptps.157.213 fatcat:exu5kqqd2rap5a32kchoriiqoi

Uncertain Distribution-Minimum Spanning Tree Problem

Jian Zhou, Xiajie Yi, Ke Wang, Jing Liu
2016 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
It is shown that the β-distribution-UMST is just the uncertain expected minimum spanning tree when β = 0.  ...  On the basis of this new concept, the definition of uncertain distribution-minimum spanning tree is proposed in three ways.  ...  Fig. 4 . 4 Uncertain β-distribution minimum spanning tree.  ... 
doi:10.1142/s0218488516500264 fatcat:lkvoame6nfegjiji6eonx76j34

The Complexity and Algorithm for Minimum Expense Spanning Trees

Zhan Ning, Wu Longshu
2012 Procedia Engineering  
In this paper, we consider the computational complexity of the minimum expense spanning tree problem, which is to find a spanning tree in a network with minimum total expenses.  ...  The minimum spanning tree problem is a classical and well-known combinatorial optimization problem. There exist many efficient algorithms such as the Kruskal algorithm and Prim algorithm to solve it.  ...  The theory of minimum expense spanning trees is developed from the cost of degree, distance, delay and so on. Usually, the cost of vertex exists independently.  ... 
doi:10.1016/j.proeng.2011.12.679 fatcat:j5usg363evcbfaymveqdkvxrtm

A weighted coding in a genetic algorithm for the degree-constrained minimum spanning tree problem

Günther R. Raidl, Bryant A. Julstrom
2000 Proceedings of the 2000 ACM symposium on Applied computing - SAC '00  
This paper describes a novel coding of spanning trees in a genetic algorithm for the degree-constrained minimum spanning tree problem.  ...  On a set of hard graphs whose unconstrained minimum spanning trees are of high degree, a genetic algorithm that uses this coding identifies degree-constrained minimum spanning trees that are on average  ...  In this case, a minimum spanning tree on n points may have degree up to n − 1.  ... 
doi:10.1145/335603.335888 dblp:conf/sac/RaidlJ00 fatcat:32dxoska6zf6ndsipkem2m6pmm

A Maximum Degree Self-Stabilizing Spanning Tree Algorithm [chapter]

Deniz Cokuslu, Kayhan Erciyes, Abdelkader Hameurlain
2010 Lecture Notes in Electrical Engineering  
spanning tree construction algorithm which uses maximum degree heuristic while choosing the root node.  ...  Spanning trees are fundamental topological structures in distributed environments which ease many applications that require frequent communication between nodes.  ...  Moreover, by using heuristics, resulting spanning trees can be tuned according to specific purposes.  ... 
doi:10.1007/978-90-481-9794-1_73 fatcat:klcaaui73bblbc34ryemd5enbu

Distributed Search for Balanced Energy Consumption Spanning Trees in Wireless Sensor Networks

Andrei Gagarin, Sajid Hussain, Laurence T. Yang
2009 2009 International Conference on Advanced Information Networking and Applications Workshops  
The approach is a modification of Kruskal's minimum spanning tree (MST) search algorithm and is based on a distributed search by hierarchical clusters.  ...  It provides spanning trees with a lower maximum degree, a bigger diameter and can be used for balanced energy consumption routing in wireless sensor networks (WSNs).  ...  Our distributed heuristic strategy is to find a spanning tree by searching for "best possible" minimum spanning tree extensions in hierarchical clusters.  ... 
doi:10.1109/waina.2009.194 dblp:conf/aina/GagarinHY09 fatcat:opocg73vrfecjoo3kt7towlw3a
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