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Linear Verification For Spanning Trees

1984
*
25th Annual Symposium onFoundations of Computer Science, 1984.
*

This leads to a

doi:10.1109/sfcs.1984.715916
dblp:conf/focs/Komlos84
fatcat:pmwybdltwnc2jfhcz6ipmjcxre
*spanning**tree**verification*algorithm using O(n -e ) comparisons in a graph with n vertices and e edges. No implementation is offered. ... Given a rooted*tree*with values associated with the n pertices and a set A of 'directed paths (queries), we describe an algorithm which finds the maximum value of every one of the given paths, and which ... A 1*for*1 A ~ : , > n. thus the*linear*term O(e)*for*the*tree**verification*problem ( j A ! en + l ) comes from the comparisons made between the maxima in A and the outside edges. ...##
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Linear verification for spanning trees

1985
*
Combinatorica
*

' Here we describe an algorithm which finds maxima over wlrious paths o f a

doi:10.1007/bf02579443
fatcat:myornxm4ybfzthp7mipaftmppu
*tree*, which leads to a minimal*spanning**tree**verification*algorithm with a*linear*number o f comparisons. ... Whatever cost we obtain*for*this directed path problem, we only need 2 ( e -~, + I) extra comparisons*for*the*spanning**tree**verification*problem. ...##
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Randomized minimum spanning tree algorithms using exponentially fewer random bits

2008
*
ACM Transactions on Algorithms
*

The prominent exception -and the main focus of this paper -is a

doi:10.1145/1328911.1328916
fatcat:mytnhdzm7fc75huzde36ger27y
*linear*-time randomized minimum*spanning**tree*algorithm that is not derived from the well known Karger-Klein-Tarjan algorithm. ... Among these are the minimum*spanning**tree*(MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel minimum*spanning**tree*problems, and the local sorting and set ... Randomized Minimum*Spanning**Tree*Algorithms · 27 ACKNOWLEDGMENTS We would like to thank David Zuckerman*for*his helpful suggestions. ...##
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Recognition of DFS trees: sequential and parallel algorithms with refined verifications

1993
*
Discrete Mathematics
*

Therefore, the question: Given an undirected graph G = (V, E) and an undirected

doi:10.1016/0012-365x(93)90375-4
fatcat:winug53ev5apznrs23fqnqe53m
*spanning**tree*r, is T a DFS*tree*(T-DFS) in G? was naturally raised and answered by sequential*linear*-time algorithms. ... In a previous work we have shown that the family of graphs in which every*spanning**tree*is a DFS*tree*is quite limited. ... This also enables us to simplify the optimal negative*verification*we had*for*this algorithm. We thank Michael Kaminski*for*pointing out some references on the complexity of matrix multiplication. ...##
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Page 4973 of Mathematical Reviews Vol. , Issue 86k
[page]

1986
*
Mathematical Reviews
*

(H-AOS)

*Linear**verification**for**spanning**trees*. Combinatorica 5 (1985), no. 1, 57-65. ... This leads to a*spanning**tree**verification*algorithm using O(n + e) comparisons in a graph with n vertices and e edges. Fan R. K. ...##
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Sensitivity Analysis of Minimum Spanning Trees in Sub-Inverse-Ackermann Time
[article]

2014
*
arXiv
*
pre-print

We present a deterministic algorithm

arXiv:1407.1910v1
fatcat:6lvaiyot2fgljhpzu7lwgxpzx4
*for*computing the sensitivity of a minimum*spanning**tree*(MST) or shortest path*tree*in O(mα(m,n)) time, where α is the inverse-Ackermann function. ... Together with the randomized*linear*time MST algorithm of Karger, Klein, and Tarjan, this gives another randomized*linear*time MST sensitivity algoritm. ... I thank Bob Tarjan*for*encouraging me to finally publish the complete version of this paper. ...##
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Inheritance Operations in Massively Parallel Knowledge Representation
[chapter]

1994
*
Machine Intelligence and Pattern Recognition
*

We present a massively parallel representation of transitive relations, emphasizing the subclass relation, which extends our previous

doi:10.1016/b978-0-444-81704-4.50011-9
fatcat:2voe6mwbwbbzfom5qoty6bqsdq
*linear**tree*representation of class hierarchies. ... A*linear*graph representation is generated by a left-to-right preorder traversal of the*spanning**tree*. ... Lemma 3b: Once the*spanning**tree*has been established, the non-*tree*arcs of a graph have no influence on the*tree*pairs. ...##
###
Sensitivity Analysis of Minimum Spanning Trees in Sub-Inverse-Ackermann Time

2015
*
Journal of Graph Algorithms and Applications
*

We present a deterministic algorithm

doi:10.7155/jgaa.00365
fatcat:wnm235bunjfwdddo5jvvzw43wm
*for*computing the sensitivity of a minimum*spanning**tree*(MST) or shortest path*tree*in O(m log α(m, n)) time, where α is the inverse-Ackermann function. ... Together with the randomized*linear*time MST algorithm of Karger, Klein, and Tarjan, this gives another randomized*linear*time MST sensitivity algorithm. ... Acknowledgements I thank Bob Tarjan*for*encouraging me to publish the complete version of this paper. ...##
###
Sensitivity Analysis of Minimum Spanning Trees in Sub-inverse-Ackermann Time
[chapter]

2005
*
Lecture Notes in Computer Science
*

We present a deterministic algorithm

doi:10.1007/11602613_96
fatcat:7nnugmbvdfbxzobwtwkb3wo3ju
*for*computing the sensitivity of a minimum*spanning**tree*(MST) or shortest path*tree*in O(m log α(m, n)) time, where α is the inverse-Ackermann function. ... Together with the randomized*linear*time MST algorithm of Karger, Klein, and Tarjan, this gives another randomized*linear*time MST sensitivity algorithm. ... Acknowledgements I thank Bob Tarjan*for*encouraging me to publish the complete version of this paper. ...##
###
An Inverse-Ackermann Type Lower Bound For Online Minimum Spanning Tree Verification*

2006
*
Combinatorica
*

Given a

doi:10.1007/s00493-006-0014-1
fatcat:nn4dulz6bbhgjc72tmcn4zgsbm
*spanning**tree*T of some graph G, the problem of minimum*spanning**tree**verification*is to decide whether T = MST (G). ... Somewhat unexpectedly, MST*verification*turns out to be useful in actually computing minimum*spanning**trees*from scratch. ... I thank Vijaya Ramachandran*for*many helpful comments, and Stephen Alstrup, Theis Rauhe, and Uri Zwick*for*reintroducing me to this problem. ...##
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A randomized linear-time algorithm to find minimum spanning trees

1995
*
Journal of the ACM
*

The algorithm uses random sampling in combination with a recently discovered

doi:10.1145/201019.201022
fatcat:krgdopuujfg5rcji5chxpli7hq
*linear*-time algorithm*for*verifying a minimum*spanning**tree*. ... We present a randomized*linear*-time algorithm to find a minimum*spanning**tree*in a connected graph with edge weights. ... We thank Rajeev Motwani, Satish Rae, and David Zuckerman*for*fruitful discussions. ...##
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Extending the Limits of Ensemble Forecast Verification with the Minimum Spanning Tree

2004
*
Monthly Weather Review
*

spaces, including those of the

doi:10.1175/1520-0493(2004)132<1522:etloef>2.0.co;2
fatcat:kjjdnq5pjvcxhcxwhv6pt2lfsi
*verifications**for*10 6 dimensional numerical weather prediction forecasts. ... Current rank histogram ensemble*verification*techniques can only evaluate scalars drawn from ensembles and associated*verification*; a new method is presented that allows*verification*in high-dimensional ... Smith*for*valuable conversations about ensemble assessment, and thank the Newton Institute at Cambridge University. The comments of two anonymous reviewers greatly enhanced the manuscript. ...##
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On Distributed Verification
[chapter]

2006
*
Lecture Notes in Computer Science
*

This talk was intended to give a partial survey and to motivate further studies of distributed

doi:10.1007/11947950_12
fatcat:6xofi2kyvfc6dgwi7wgf7o3v5a
*verification*. ... In this paper we explain some motivations*for*specific definitions, survey some very related notions and their motivations in the literature, survey some examples*for*problems and solutions, and mention ... In the simple model*for*local*verification*, both the*spanning**tree*and the MST*verification*problems require Ω(n) time rounds. Sketch of Proof: We show the result*for*the*spanning**tree*case. ...##
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Tight Bounds For Distributed MST Verification

2011
*
Symposium on Theoretical Aspects of Computer Science
*

This paper establishes tight bounds

doi:10.4230/lipics.stacs.2011.69
dblp:conf/stacs/KorKP11
fatcat:wres5yaaijhkpixd6qafqgxkfe
*for*the Minimum-weight*Spanning**Tree*(MST)*verification*problem in the distributed setting. ... Our upper bound result appears to indicate that the*verification*of an MST may be easier than its construction, since*for*MST construction, both lower bounds of Ω(|E|) messages and Ω( √ n+D) time hold, ... The distributed MST*Verification*problem Formally, the minimum-weight*spanning**tree*(MST)*verification*problem can be stated as follows. ...##
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Page 2263 of Mathematical Reviews Vol. , Issue 94d
[page]

1994
*
Mathematical Reviews
*

Therefore, the question: Given an undirected graph G = (V, E) and an undirected

*spanning**tree*T, is T a DFS*tree*(J-DFS) in G? was naturally raised and answered by sequential*linear*-time algorithms. ... “In a previous work we showed that the family of graphs in which every*spanning**tree*is a DFS*tree*is quite limited. ...
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