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The Distributed Minimum Spanning Tree Problem

Gopal Pandurangan, Peter Robinson, Michele Scquizzato
2018 Bulletin of the European Association for Theoretical Computer Science  
This article surveys the distributed minimum spanning tree (MST) problem, a central and one of the most studied problems in distributed computing.  ...  This article summarizes the long line of research in designing efficient distributed algorithms and showing lower bounds for the distributed MST problem, including the most recent developments which have  ...  that run faster and output an approximate minimum spanning tree.  ... 
dblp:journals/eatcs/Pandurangan0S18 fatcat:2gsu4hkhq5bvbbydiwmp6osppi

Clustering, Randomness, and Regularity: Spatial Distributions and Human Performance on the Traveling Salesperson Problem and Minimum Spanning Tree Problem

Matthew Dry, Kym Preiss, Johan Wagemans
2012 Journal of Problem Solving  
We investigated human performance on the Euclidean Traveling Salesperson Problem (TSP) and Euclidean Minimum Spanning Tree Problem (MST-P) in regards to a factor that has previously received little attention  ...  within the literature: the spatial distributions of TSP and MST-P stimuli.  ...  , where the number of potential intersections is given by A related problem to the TSP is the Minimum Spanning Tree Problem (MST-P).  ... 
doi:10.7771/1932-6246.1117 fatcat:u52afxdwzzhyxckvan5w4rfsfm

Parallel Minimum Spanning Tree Heuristic for the steiner problem in graphs

H. Akbari, Z. Iranmanesh, M. Ghodsi
2007 2007 International Conference on Parallel and Distributed Systems  
Minimum Spanning Tree Heuristic (MSTH) is a heuristic for solving the Steiner problem in graphs. In this paper we first review existing algorithms for solving the Steiner problem in graphs.  ...  Given an undirected graph with weights associated with its edges, the Steiner tree problem consists of finding a minimum weight subtree spanning a given subset of (terminal) nodes of the original graph  ...  When |N| = 2 the problem reduces to the shortest path problem while when N = V the problem reduces to the minimum spanning tree problem. Both these problems can be solved in polynomial time.  ... 
doi:10.1109/icpads.2007.4447726 dblp:conf/icpads/AkbariIG07 fatcat:rhlkovpeubh57d5x2hoafijk2e

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

Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems

B. Awerbuch
1987 Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87  
Those problems include Minimum-Weight Spanning Tree (MST), Leader Election, counting the number of network nodes, and computing a senaitive decomposable function (e.g. majority, parity, maximum, OR, AND  ...  This problem, which has been known for at least 9 years, is one of the most fundamental and the most studied problems in the field of distributed network algorithms.  ...  Acknowledgements Oded Goldreich and Silvio Micali have collaborated with the author in the earlier stages of this research and contributed some of the ideas used in the Counting Algorithm.  ... 
doi:10.1145/28395.28421 dblp:conf/stoc/Awerbuch87 fatcat:3zb7nf4pf5ebnjeoovifxoeume

Unconditional lower bounds on the time-approximation tradeoffs for the distributed minimum spanning tree problem

Michael Elkin
2004 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04  
In this paper we initiate the systematic study of this subject, and show strong unconditional lower bounds on the time-approximation tradeoff of the distributed minimum spanning tree problem, and some  ...  However, so far little progress was done in the study of the hardness of distributed approximation.  ...  Acknowledgements: The author is grateful to Michael Langberg, Zvika Lotker, Alessandro Panconesi, David Peleg, Alexander Razborov, Oded Regev, Vitaly Rubinovich and Avi Wigderson for helpful discussions  ... 
doi:10.1145/1007352.1007407 dblp:conf/stoc/Elkin04 fatcat:6y7k2lp4tjbdzo7af65buplj2i

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

Optimal algorithms for the vertex updating problem of a minimum spanning tree

D.B. Johnson, P. Metaxas
Proceedings Sixth International Parallel Processing Symposium  
The vertex updating problem for a minimum spanning tree (MST) is de ned as follows: Given a graph G = (V; E G ) and its MST T, update T when a new vertex z is introduced along with weighted edges that  ...  These rules can also be used to derive simple linear-time sequential algorithms for the same problem.  ...  The authors would like to thank Professors Sam Bent and Jim Driscoll for their helpful comments on the presentation of the paper.  ... 
doi:10.1109/ipps.1992.223028 dblp:conf/ipps/JohnsonM92 fatcat:lbcxo7hezvgx3mkyhuqm2xcpc4

Uncertain Quadratic Minimum Spanning Tree Problem

Jian Zhou, Xing He, Ke Wang
2014 Journal of Communications  
The quadratic minimum spanning tree problem is to find a spanning tree on a graph that minimizes a quadratic objective function of the edge weights.  ...  It is shown that the problem of finding an uncertain quadraticminimum spanning tree can be handled in the framework of the deterministic quadratic minimum spanning tree problem requiring no particular  ...  ACKNOWLEDGMENT The authors are grateful to the anonymous referees for their valuable comments and suggestions to improve the presentation of this paper.  ... 
doi:10.12720/jcm.9.5.385-390 fatcat:rnvir43d4ra7fh7af7htkrcrbq

The Inverse Spanning Tree of a Fuzzy Graph Based on Credibility Measure

Jian Zhou, Qina Wang, Xiang Zhang
2013 Journal of Communications  
An inverse spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree.  ...  In this paper, based on the notion of fuzzy α-minimum spanning tree, the inverse spanning tree problem with fuzzy edge weights is discussed and formulated as a fuzzy programming model with some chance  ...  They also provided the other two new definitions, i.e., the expected minimum spanning tree and the most minimum spanning tree, for the fuzzy minimum spanning tree problem.  ... 
doi:10.12720/jcm.8.9.566-571 fatcat:24wsznypv5fn7jxw7qob6gjgbe

A Chance-Constrained Programming Model for Inverse Spanning Tree Problem with Uncertain Edge Weights

Xiang Zhang, Qina Wang, Jian Zhou
2013 International Journal of Advancements in Computing Technology  
The inverse spanning tree problem is to make a given spanning tree be a minimum spanning tree on a connected graph via a minimum perturbation on its edge weights.  ...  It is shown that such an uncertain minimum spanning tree can be characterized by some constraints on the paths of the graph.  ...  Introduction The inverse spanning tree problem or inverse minimum spanning tree problem is a type of inverse optimization problems.  ... 
doi:10.4156/ijact.vol5.issue6.10 fatcat:xqn7yz3n2fdtjjsjc36pn5wl3e

Spanning tree problem of uncertain network

Jin Peng, Shengguo Li
2012 2012 2nd International Conference on Applied Robotics for the Power Industry (CARPI)  
In this paper we consider a spanning tree problem of uncertain network, which is a natural uncertain variation of the deterministic minimum spanning tree problem.  ...  By means of uncertainty theory, we propose three types of minimum spanning tree models for uncertain network, i.e., expected minimum spanning tree, α-minimum spanning tree, and distribution minimum spanning  ...  In Section 4, three types of minimum spanning tree models for UST problem are presented, which includes expected minimum spanning tree, α-minimum spanning tree and distribution minimum spanning tree.  ... 
doi:10.1109/carpi.2012.6356407 fatcat:vj5jc4eyfvawhjo4sgxccji33y

Uncertain Distribution-Minimum Spanning Tree Problem

Jian Zhou, Xiajie Yi, Ke Wang, Jing Liu
2016 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
This paper studies the minimum spanning tree problem on a graph with uncertain edge weights, which are formulated as uncertain variables.  ...  It is shown that the β-distribution-UMST is just the uncertain expected minimum spanning tree when β = 0.  ...  Uncertain Distribution-Minimum Spanning Tree Problem 541 Classical minimum spanning tree problem Following many earlier studies on the MST problem (e.g.  ... 
doi:10.1142/s0218488516500264 fatcat:lkvoame6nfegjiji6eonx76j34

Path Optimality Conditions for Minimum Spanning Tree Problem with Uncertain Edge Weights

Jian Zhou, Lu Chen, Ke Wang
2015 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
, namely, the uncertain expected minimum spanning tree (expected UMST), the uncertain αminimum spanning tree (α-UMST), and the uncertain distribution minimum spanning tree.  ...  Recently, Zhang et al. 20 studied the inverse minimum spanning tree problem, and Zhou et al. 21 introduced the uncertain quadratic minimum spanning tree problem.  ...  Acknowledgements This work was supported in part by grants from the National Social Science Foundation of China (No. 13CGL057), and the Shanghai Philosophy and Social Science Planning Project (No. 2012BGL006  ... 
doi:10.1142/s0218488515500038 fatcat:cm2dggcmm5g3ffti5v3luuxw2q

A learning automata-based heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs

Javad Akbari Torkestani, Mohammad Reza Meybodi
2010 Journal of Supercomputing  
In this paper, we propose a learning automata-based heuristic algorithm to solve the minimum spanning tree problem in stochastic graphs wherein the probability distribution function of the edge weight  ...  This is due to the fact that the minimum spanning tree problem becomes incredibly hard to solve when the edge weight is assumed to be a random variable.  ...  Minimum spanning tree problem The Minimum Spanning Tree problem is a classical combinatorial optimization problem in graph theory.  ... 
doi:10.1007/s11227-010-0484-1 fatcat:lpg2w3664rctrjcmj4pk37p7sm
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