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The Distributed Minimum Spanning Tree Problem

2018
*
Bulletin of the European Association for Theoretical Computer Science
*

This article surveys

dblp:journals/eatcs/Pandurangan0S18
fatcat:2gsu4hkhq5bvbbydiwmp6osppi
*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*. ...##
###
Clustering, Randomness, and Regularity: Spatial Distributions and Human Performance on the Traveling Salesperson Problem and Minimum Spanning Tree Problem

2012
*
Journal of Problem Solving
*

We investigated human performance on

doi:10.7771/1932-6246.1117
fatcat:u52afxdwzzhyxckvan5w4rfsfm
*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). ...##
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Parallel Minimum Spanning Tree Heuristic for the steiner problem in graphs

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. ...

##
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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

doi:10.1142/s0129054104002571
fatcat:hbuqxxql55c7vd5nudxr3j4zea
*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). ...##
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Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems

1987
*
Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87
*

Those

doi:10.1145/28395.28421
dblp:conf/stoc/Awerbuch87
fatcat:3zb7nf4pf5ebnjeoovifxoeume
*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. ...##
###
Unconditional lower bounds on the time-approximation tradeoffs for the distributed minimum spanning tree problem

2004
*
Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04
*

In this paper we initiate

doi:10.1145/1007352.1007407
dblp:conf/stoc/Elkin04
fatcat:6y7k2lp4tjbdzo7af65buplj2i
*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 ...##
###
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

doi:10.1109/ipdps.2003.1213299
dblp:conf/ipps/BlinB03
fatcat:4ejuu4shcve7nlpdt2jjsms5ya
*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). ...##
###
Optimal algorithms for the vertex updating problem of a minimum spanning tree

*
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. ...

##
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Uncertain Quadratic Minimum Spanning Tree Problem

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. ...

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

2013
*
Journal of Communications
*

An inverse

doi:10.12720/jcm.8.9.566-571
fatcat:24wsznypv5fn7jxw7qob6gjgbe
*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*. ...##
###
A Chance-Constrained Programming Model for Inverse Spanning Tree Problem with Uncertain Edge Weights

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*. ...

##
###
Spanning tree problem of uncertain network

2012
*
2012 2nd International Conference on Applied Robotics for the Power Industry (CARPI)
*

In this paper we consider a

doi:10.1109/carpi.2012.6356407
fatcat:vj5jc4eyfvawhjo4sgxccji33y
*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*. ...##
###
Uncertain Distribution-Minimum Spanning Tree Problem

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

This paper studies

doi:10.1142/s0218488516500264
fatcat:lkvoame6nfegjiji6eonx76j34
*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. ...##
###
Path Optimality Conditions for Minimum Spanning Tree Problem with Uncertain Edge Weights

2015
*
International Journal of Uncertainty Fuzziness and Knowledge-Based Systems
*

, namely,

doi:10.1142/s0218488515500038
fatcat:cm2dggcmm5g3ffti5v3luuxw2q
*the*uncertain expected*minimum**spanning**tree*(expected UMST),*the*uncertain α*minimum**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 ...##
###
A learning automata-based heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs

2010
*
Journal of Supercomputing
*

In this paper, we propose a learning automata-based heuristic algorithm to solve

doi:10.1007/s11227-010-0484-1
fatcat:lpg2w3664rctrjcmj4pk37p7sm
*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. ...
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