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A Linear Time Algorithm for Finding Minimum Spanning Tree Replacement Edges
[article]

2020
*
arXiv
*
pre-print

Given

arXiv:1908.03473v3
fatcat:hclzzvnynzgtlap2cf5pnbbyf4
*an*undirected, weighted graph, the*minimum**spanning**tree*(MST) is a*tree*that connects all of the vertices of the graph with*minimum*sum of edge weights. ... Given the MST and sorted non-*tree*edges, our*algorithm*is the first that runs in*O*(m+n) time and*O*(m+n) space to*find*all replacement edges. ... Thus, our approach will also*find*the most vital edge in*O*(m + n) time, and is the first linear*algorithm**for**finding*the most vital edge of the*minimum**spanning**tree*given the non-*tree*edges sorted by ...##
###
Linear Time Algorithms Based on Multilevel Prefix Tree for Finding Shortest Path with Positive Weights and Minimum Spanning Tree in a Networks
[article]

2007
*
arXiv
*
pre-print

In this paper I present general outlook on questions relevant to the basic graph

arXiv:0708.3408v1
fatcat:othcbvqw6vb2ditml2kkxpndty
*algorithms*;*Finding*the Shortest Path with Positive Weights and*Minimum**Spanning**Tree*. ... It should be noticed that the*algorithms*which compute the Shortest Path and*Minimum**Spanning**Tree*problems not only analyze the weight of arcs (which is the main and often the only criterion of solution ... If Q is implemented as a binary min-heap, the total time*for*Jarnik-Prim's*algorithm*is*O*(|*V*|*log*|*V*| + |*E*|*log*|*V*|) =*O*(|*E*|*log*|*V*|). ...##
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Efficient Algorithms for Finding the k Most Vital Edges for the Minimum Spanning Tree Problem
[chapter]

2011
*
Lecture Notes in Computer Science
*

We study in this paper the problem of

doi:10.1007/978-3-642-22616-8_11
fatcat:yhkhls74djh5fkor35uq4fg6bm
*finding*in a graph a subset of k edges whose deletion causes the largest increase in the weight of a*minimum**spanning**tree*. ... We propose*for*this problem*an*explicit enumeration*algorithm*whose complexity, when compared to the current best*algorithm*, is better*for*general k but very slightly worse*for*fixed k. ... The sensitivity of a*minimum**spanning**tree*T , i.e. the allowable variation*for*each edge weight so that T remains a*minimum**spanning**tree*, can be computed in*O*(m*log*α(m, n)) [12] . ...##
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An ant-based algorithm for finding degree-constrained minimum spanning tree

2006
*
Proceedings of the 8th annual conference on Genetic and evolutionary computation - GECCO '06
*

In this paper we give

doi:10.1145/1143997.1144000
dblp:conf/gecco/BuiZ06
fatcat:c27tmot3srbo5pupq26qwr3yay
*an*Ant-Based*algorithm**for**finding*low cost degree-constrained*spanning**trees*. ... The problem of*finding*the degree-constrained*spanning**tree*of*minimum*cost in*an*edge weighted graph is well known to be NP-hard. ... We also would like to thank the anonymous reviewers*for*their helpful comments. ...##
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A Distributed Algorithm for Finding All Best Swap Edges of a Minimum-Diameter Spanning Tree

2011
*
IEEE Transactions on Dependable and Secure Computing
*

*algorithms*

*for*two variants of this problem. ... Finally, we consider the computation of swap edges in

*an*arbitrary

*spanning*

*tree*, where swap edges are chosen to minimize the time required to adapt routing in case of a failure, and give efficient distributed ...

*For*shortest paths

*trees*(as opposed to

*minimum*diameter

*spanning*

*trees*),

*an*earlier centralized

*algorithm*[5] has been complemented by a distributed

*algorithm*using techniques

*for*

*finding*all best swap ...

##
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An Õ(n2) algorithm for minimum cuts

1993
*
Proceedings of the twenty-fifth annual ACM symposium on Theory of computing - STOC '93
*

The rst is

doi:10.1145/167088.167281
dblp:conf/stoc/KargerS93
fatcat:qvxuxlalbnhbdhh4g2bojq6guy
*an*(m 2 =n)-processor N C*algorithm**for*nding a (2 + )-approximation to the*minimum*cut. ... Another application of these techniques yield*an*N C*algorithm**for*nding a sparse kconnectivity certi cate*for*all polynomially bounded values of k. ...*For*each edge*e*in G that connects*trees*T and U, we add*an*edge*e*F connecting*v*T and*v*U . Thus, the reduced graph is what we get if we start with G and contract all the forest edges. ...##
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An O(logn)-Competitive Algorithm for Online Constrained Forest Problems
[chapter]

2011
*
Lecture Notes in Computer Science
*

Agrawal, Klein, and Ravi [1] give a 2-approximation

doi:10.1007/978-3-642-22006-7_4
fatcat:5y4wvyfq5bfpdpfgrfkc36iiz4
*algorithm**for*the offline problem; Berman and Coulston [3] give*an**O*(*log*n)-competitive*algorithm**for*the online problem. ... In this paper, we show how to combine the ideas of Goemans and Williamson and those of Berman and Coulston to give*an**O*(*log*n)-competitive*algorithm**for*online constrained forest problems, including*an*... The goal of the Steiner*tree*problem is to*find*a*minimum*-cost*tree*T that*spans*all the terminals R. ...##
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An O(log n/log log n)-Approximation Algorithm for the Asymmetric Traveling Salesman Problem

2017
*
Operations Research
*

We present a randomized

doi:10.1287/opre.2017.1603
fatcat:krwti2dm55bcfdrylbzspqcv5m
*O*(*log*n/*log**log*n)-approximation*algorithm**for*the asymmetric traveling salesman problem (ATSP). ... The key ingredient of our approach is a new connection between the approximability of the ATSP and the notion of so-called thin*trees*. ...*Algorithm*1 1*An**O*(*log*n/*log**log*n)-approximation*algorithm**for*the ATSP. Input: A set*V*consisting of n points and a cost function c :*V*×*V*→ R + satisfying the triangle inequality. ...##
###
An algorithmic approach for finding minimum spanning tree in a intuitionistic fuzzy graph

unpublished

We define this problem as intuitionistic

doi:10.29007/sx3s
fatcat:cwr3x6t7vrbmjextozuyqcuhgu
*minimum**spanning**tree*(IMST) problem. We introduce*an**algorithmic*approach*for*designing the IMST of a fuzzy. ... The*minimum**spanning**tree*(MST) problem is a well known optimization problem in graph theory that has been used to model many real life problems, e.g., telecommuni- cations,transportation network, routing ... Modified Boruvka's*Algorithm**for*IMST The classical Boruvka's*algorithm*is a well known greedy method*for**finding*the MST of a connected graph and the time complexity of this*algorithm*is*O*(m*log*n) time ...##
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An O(n2(m + n log n) log n) min-cost flow algorithm

1986
*
27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
*

Galil and

doi:10.1109/sfcs.1986.7
dblp:conf/focs/GalilT86
fatcat:p2kx3ty64rflxfnhtlvta6vbz4
*E*. Tardos,*An**O*(n 2 (m + n*log*n) logn) min-cost flow*algorithm*. ... In this paper we design*an**O*( n 2 ( m + n*log*n)*log*n)*algorithm*. The previous best*algorithm*had*an**O*( m 2 ( m+n*log*n)*log*n) time bound. ... By Corollary 5.2 we know that Step 1 is executed at most 2m times, each time computing maximum weight*spanning**tree*in time Oem*log*n) [Tn]*for*a total of*O*(m 2 logn). ...##
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An almost O (log k )-approximation for k -connected subgraphs

2009
*
ACM-SIAM Symposium on Discrete Algorithms
*

We consider two cases of the Survivable Network Design (SND) problem: given a complete graph G n = (

dblp:conf/soda/Nutov09
fatcat:t7y7cquznzek5cdcny3gwvmw2q
*V*,*E*n ) with costs on the edges and connectivity requirements {r(u,*v*) : u,*v*∈*V*},*find*a*minimum*... Our main result is*an**O**log*k •*log*n n−kapproximation*algorithm**for*the k-Connected Subgraph problem (the case r(u,*v*) = k*for*all u,*v*∈*V*),*for*both directed and undirected graphs, where n = |*V*|. ... Objective:*Find*a*minimum*cost k-connected*spanning*subgraph G of G n . ...##
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Construction and impromptu repair of an MST in a distributed network with o(m) communication
[article]

2015
*
arXiv
*
pre-print

knows n, then there are Monte Carlo

arXiv:1502.03320v1
fatcat:ayoprojkifdqjmwdjv4pnftzte
*algorithms*which succeed w.h.p. to determine a*minimum**spanning*forest (MST) and a*spanning*forest (ST) using*O*(n ^2 n/ n) messages*for*MST and*O*(n n ) messages*for*... Previous*algorithms**for*this problem that use*an*amortized*o*(m) messages per update require substantial preprocessing and additional local storage between updates. ... We show that*O*(*log*n/*log**log*n) broadcast-and-echoes suffice. In the previous subsection, the*log*n-wise "pivots" were chosen obliviously. Here, we use pivots based on randomly chosen edges. ...##
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An O(n logn) heuristic for steiner minimal tree problems on the euclidean metric

1981
*
Networks
*

*An*

*O*(n

*log*n) heuristic

*for*the Euclidean Steiner Minimal

*Tree*(ESMT) problem is presented. ... to the Voronoi diagram and

*Minimum*

*Spanning*

*Tree*(MST) of the point set. ... The authors would like to thank the referees

*for*their valuable criticism and the Graduate Research Board of the University of Illinois

*for*providing the necessary funds

*for*conducting the computer experiments ...

##
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A Distributed Algorithm for Finding All Best Swap Edges of a Minimum Diameter Spanning Tree
[chapter]

*
Lecture Notes in Computer Science
*

*algorithms*

*for*two variants of this problem. ... Finally, we consider the computation of swap edges in

*an*arbitrary

*spanning*

*tree*, where swap edges are chosen to minimize the time required to adapt routing in case of a failure, and give efficient distributed ... ACKNOWLEDGEMENTS We would like to thank the anonymous reviewers

*for*their comments, which helped to improve the presentation of this work. ...

##
###
An O(1)-Approximation for Minimum Spanning Tree Interdiction
[article]

2015
*
arXiv
*
pre-print

One of the oldest and best-studied interdiction problems is

arXiv:1508.01448v1
fatcat:aqzvifux2bbz7dt7b7p7qhm45y
*minimum**spanning**tree*(MST) interdiction. ... Frederickson and Solis-Oba (SODA 1996) presented*an**O*(*log*m)-approximation*for*MST interdiction, where m is the number of edges. ... Ravi, and the anonymous reviewers*for*many helpful comments. ...
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