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Distributed Algorithms for Minimum Degree Spanning Trees
[article]

2018
*
arXiv
*
pre-print

The

arXiv:1806.03365v1
fatcat:mnoho7zkevfv5ndztigcbwo7je
*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 ...##
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A distributed approximation algorithm for the minimum degree minimum weight spanning trees
[article]

2006
*
arXiv
*
pre-print

Fischer has shown how to compute a

arXiv:cs/0607031v1
fatcat:vtrsyxdl7za4fjg4wmni4j6cmi
*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. ...##
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A distributed approximation algorithm for the minimum degree minimum weight spanning trees

2008
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Journal of Parallel and Distributed Computing
*

Fischer [3] has shown how to compute a

doi:10.1016/j.jpdc.2007.07.005
fatcat:nrzhl3nwoze4hmh2oillzyr5hy
*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. ...##
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Self-stabilizing minimum degree spanning tree within one from the optimal degree

2011
*
Journal of Parallel and Distributed Computing
*

We propose a self-stabilizing algorithm for constructing a

doi:10.1016/j.jpdc.2010.08.019
fatcat:tspkrmzflfgfvje4rrxjuflrna
*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*. ...##
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Self-stabilizing minimum-degree spanning tree within one from the optimal degree

2009
*
2009 IEEE International Symposium on Parallel & Distributed Processing
*

We propose a self-stabilizing algorithm for constructing a

doi:10.1109/ipdps.2009.5161042
dblp:conf/ipps/BlinPR09
fatcat:rkazjvg5nbb65pcogmn3jp4zwi
*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*. ...##
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THE FIRST APPROXIMATED DISTRIBUTED ALGORITHM FOR THE MINIMUM DEGREE SPANNING TREE PROBLEM ON GENERAL GRAPHS

2004
*
International Journal of Foundations of Computer Science
*

In this paper we present the first

doi:10.1142/s0129054104002571
fatcat:hbuqxxql55c7vd5nudxr3j4zea
*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). ...##
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Self-stabilizing minimum-degree spanning tree within one from the optimal degree Self-stabilizing minimum-degree spanning tree within one from the optimal degree

2009
*
IEEE International Symposium on Parallel&Distributed Processing
*
unpublished

We propose a self-stabilizing algorithm for constructing a

fatcat:ucxn4sffubg5rbzk6l2pgntbfy
*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*. ...##
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The first approximated distributed algorithm for the minimum degree spanning tree problem on general graphs

*
Proceedings International Parallel and Distributed Processing Symposium
*

In this paper we present the first

doi:10.1109/ipdps.2003.1213299
dblp:conf/ipps/BlinB03
fatcat:4ejuu4shcve7nlpdt2jjsms5ya
*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). ...##
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Scale-Free spanning trees of complex networks

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. ...

##
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Underlying Scale-Free Trees in Complex Networks

2005
*
Progress of Theoretical Physics Supplement
*

We also find that the

doi:10.1143/ptps.157.213
fatcat:exu5kqqd2rap5a32kchoriiqoi
*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. ...##
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Uncertain Distribution-Minimum Spanning Tree Problem

2016
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International Journal of Uncertainty Fuzziness and Knowledge-Based Systems
*

It is shown that the β-

doi:10.1142/s0218488516500264
fatcat:lkvoame6nfegjiji6eonx76j34
*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*. ...##
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The Complexity and Algorithm for Minimum Expense Spanning Trees

2012
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Procedia Engineering
*

In this paper, we consider the computational complexity of the

doi:10.1016/j.proeng.2011.12.679
fatcat:j5usg363evcbfaymveqdkvxrtm
*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. ...##
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A weighted coding in a genetic algorithm for the degree-constrained minimum spanning tree problem

2000
*
Proceedings of the 2000 ACM symposium on Applied computing - SAC '00
*

This paper describes a novel coding of

doi:10.1145/335603.335888
dblp:conf/sac/RaidlJ00
fatcat:32dxoska6zf6ndsipkem2m6pmm
*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. ...##
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A Maximum Degree Self-Stabilizing Spanning Tree Algorithm
[chapter]

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. ...

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

2009
*
2009 International Conference on Advanced Information Networking and Applications Workshops
*

The approach is a modification of Kruskal's

doi:10.1109/waina.2009.194
dblp:conf/aina/GagarinHY09
fatcat:opocg73vrfecjoo3kt7towlw3a
*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. ...
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