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Distributed Approximation Algorithms for Finding 2-Edge-Connected Subgraphs
[chapter]

*
Lecture Notes in Computer Science
*

A

doi:10.1007/978-3-540-77096-1_12
dblp:conf/opodis/KrumkeMNR07
fatcat:3jm3t3v2gzgqdlosgj7mzuvdv4
*2*-ECSS of a graph is a*subgraph*that,*for*each pair of vertices, contains at least two*edge*-disjoint paths*connecting*these vertices. ... We present a*distributed*3*2*-*approximation**algorithm**for*the unweighted*2*-ECSS construction problem that requires O(n) communication rounds and O(m) messages. ... Theorem*2*. [15]*Algorithm*A card is a*distributed*3*2*-*approximation**algorithm**for*unweighted*2*-ECSS construction problem. ...##
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A simple randomized scheme for constructing low-weight k-connected spanning subgraphs with applications to distributed algorithms

2007
*
Theoretical Computer Science
*

the expected message complexity of our

doi:10.1016/j.tcs.2007.05.028
fatcat:xm2rncvi7rdvrmhmrpe5lew7gq
*algorithm*is significantly better than the best*distributed**algorithm*that*finds*an optimal k-*connected**subgraph*. ... We then show that our scheme can be applied to design an efficient*distributed**algorithm**for*constructing such an*approximate*k-*connected*spanning*subgraph*(*for*any k ≥ 1) in a point-to-point*distributed*... Acknowledgments We are very grateful to the referees*for*their careful reading of the paper and detailed comments, which helped greatly in improving the presentation of the paper. ...##
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Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks

2003
*
Proceedings of the 9th annual international conference on Mobile computing and networking - MobiCom '03
*

In this case, we present simple and practical

doi:10.1145/938985.939016
dblp:conf/mobicom/HajiaghayiIM03
fatcat:cp4yokolmnbn3ixwnlcxjdjvmy
*distributed**algorithms**for*the cases of*2*-and 3-*connectivity*with constant*approximation*factors. ... We generalize this*algorithm*to obtain an O(k 2c+*2*)-*approximation**for*general k-*connectivity*(*2*≤ c ≤ 4 is the power attenuation exponent). ...*For*graphs whose*edge*lengths form a metric, we present simple and practical*distributed**algorithms*with constant*approximation*factors*for*the cases of*2*-and 3-*connectivity*. ...##
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Power Optimization in Fault-Tolerant Topology Control Algorithms for Wireless Multi-hop Networks

2007
*
IEEE/ACM Transactions on Networking
*

In this case, we present simple and practical

doi:10.1109/tnet.2007.902680
fatcat:g5y2t432pjgcndlkjkvdv7rbfy
*distributed**algorithms**for*the cases of*2*-and 3-*connectivity*with constant*approximation*factors. ... We generalize this*algorithm*to obtain an O(k 2c+*2*)-*approximation**for*general k-*connectivity*(*2*≤ c ≤ 4 is the power attenuation exponent). ...*For*graphs whose*edge*lengths form a metric, we present simple and practical*distributed**algorithms*with constant*approximation*factors*for*the cases of*2*-and 3-*connectivity*. ...##
###
Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks

2003
*
Proceedings of the 9th annual international conference on Mobile computing and networking - MobiCom '03
*

In this case, we present simple and practical

doi:10.1145/939014.939016
fatcat:tx4iw6vnz5gahcwjczcrhfxflu
*distributed**algorithms**for*the cases of*2*-and 3-*connectivity*with constant*approximation*factors. ... We generalize this*algorithm*to obtain an O(k 2c+*2*)-*approximation**for*general k-*connectivity*(*2*≤ c ≤ 4 is the power attenuation exponent). ...*For*graphs whose*edge*lengths form a metric, we present simple and practical*distributed**algorithms*with constant*approximation*factors*for*the cases of*2*-and 3-*connectivity*. ...##
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Deploying Sensor Networks With Guaranteed Fault Tolerance

2010
*
IEEE/ACM Transactions on Networking
*

We have implemented greedy and

doi:10.1109/tnet.2009.2024941
fatcat:imsothprlbfkrgcnvxwry3emnq
*distributed*versions of this*algorithm*, and demonstrate in simulation that they produce high-quality placements*for*the additional sensors. ... We design and analyze the first*algorithms*that place an almost-minimum number of additional sensors to augment an existing network into a k-*connected*network,*for*any desired parameter k. ... Our*algorithm**finds*an -*approximation*to the minimum-weight -*connected**subgraph*, and then*for*every*edge*of weight , adds sensors. ...##
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Deploying sensor networks with guaranteed capacity and fault tolerance

2005
*
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing - MobiHoc '05
*

We have implemented greedy and

doi:10.1145/1062689.1062729
dblp:conf/mobihoc/BredinDHR05
fatcat:bk4im6a3ofbjhd2opbpdokgiie
*distributed*versions of this*algorithm*, and demonstrate in simulation that they produce high-quality placements*for*the additional sensors. ... We design and analyze the first*algorithms*that place an almostminimum number of additional sensors to augment an existing network into a k-*connected*network,*for*any desired parameter k. ... Our*algorithm**finds*an α-*approximation*to the minimum-weight k-*connected**subgraph*, and then*for*every*edge*of weight w ≥ 1, adds kw + 2k −*2*< 3kw sensors. ...##
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Motif discovery algorithms in static and temporal networks: A survey

2020
*
Journal of Complex Networks
*

The complexities associated with graph and

doi:10.1093/comnet/cnaa031
fatcat:7hasephaffajdl5bn7gl33qn2a
*subgraph*isomorphism problems, as the core of frequent*subgraph*mining, directly impact the performance of motif discovery*algorithms*. ... In this article, we provide a survey of motif discovery*algorithms*proposed in the literature*for*mining static and temporal networks and review the corresponding*algorithms*based on their adopted strategies ... GRAFT [133] is another*approximate*frequency*algorithm**for*creating graphlet frequency*distribution**for**subgraph*up to five vertices. ...##
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Distributed Verification and Hardness of Distributed Approximation

2012
*
SIAM journal on computing (Print)
*

as

doi:10.1137/11085178x
fatcat:xkvkvn6hlnh6vi4f56szewjv4m
*connectivity*, spanning*connected**subgraph*, and s − t cut verification. ... Our result implies that there can be no*distributed**approximation**algorithm**for*MST that is significantly faster than the current exact*algorithm*,*for*any*approximation*factor. ... in H and*2*on other*edges*and*find*the MST using an*algorithm*in [15] . ...##
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Distributed verification and hardness of distributed approximation

2011
*
Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11
*

as

doi:10.1145/1993636.1993686
dblp:conf/stoc/SarmaHKKNPPW11
fatcat:igixoskxrbhntjdntoox7snmnq
*connectivity*, spanning*connected**subgraph*, and s − t cut verification. ... Our result implies that there can be no*distributed**approximation**algorithm**for*MST that is significantly faster than the current exact*algorithm*,*for*any*approximation*factor. ... in H and*2*on other*edges*and*find*the MST using an*algorithm*in [15] . ...##
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Large Very Dense Subgraphs in a Stream of Edges
[article]

2020
*
arXiv
*
pre-print

A

arXiv:2010.07794v1
fatcat:qd3odlcpg5gn3eq6udyc63gmve
*subgraph*S is very dense if it has Ω(|S|^*2*)*edges*. We uniformly sample the*edges*with a Reservoir of size k=O(√(n).log n). ... We study the detection and the reconstruction of a large very dense*subgraph*in a social graph with n nodes and m*edges*given as a stream of*edges*, when the graph follows a power law degree*distribution*... An Ω( ) lower bound is presented in [5]*for*the -*approximation*of the maximum density ratio * , i.e. to*find*a*subgraph*with a vertex such that ( ) ≥ * / . ...##
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Distributed Verification and Hardness of Distributed Approximation
[article]

2011
*
arXiv
*
pre-print

Our result implies that there can be no

arXiv:1011.3049v3
fatcat:wctqtam435hxldsbeh2apbt3fy
*distributed**approximation**algorithm**for*MST that is significantly faster than the current exact*algorithm*,*for*any*approximation*factor. ... as*connectivity*, spanning*connected**subgraph*, and s-t cut verification. ...*For*any Γ, d ≥*2*, p and ǫ ≥ 0, if there exists an ǫ-error*distributed**algorithm**for*the spanning*connected**subgraph*verification problem on graph G(Γ, d, p) then there exists an ǫ-error*algorithm**for*verifying ...##
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Distributed Almost Exact Approximations for Minor-Closed Families
[chapter]

2006
*
Lecture Notes in Computer Science
*

We give efficient deterministic

doi:10.1007/11841036_24
fatcat:vgji7jmjjjhu5kwdykiy75f6ki
*distributed**algorithms*which given a graph G from a proper minor-closed family C*find*an*approximation*of a minimum dominating set in G and a minimum*connected*dominating ... The*algorithms*are deterministic and run in a polylogarithmic number of rounds. The*approximation*accomplished differs from an optimal by a multiplicative factor of (1 + o(1)). ...*Distributed**approximation**algorithms**for*planar graphs were studied in [CH04] and [CHS06] . ...##
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Motif Discovery Algorithms in Static and Temporal Networks: A Survey
[article]

2020
*
arXiv
*
pre-print

The complexities associated with graph and

arXiv:2005.09721v1
fatcat:m7ytgi2kajcsdoj2cgz2nba6uy
*subgraph*isomorphism problems, as the core of frequent*subgraph*mining, have direct impacts on the performance of motif discovery*algorithms*. ... In this paper, we provide a survey of motif discovery*algorithms*proposed in the literature*for*mining static and temporal networks and review the corresponding*algorithms*based on their adopted strategies ... Any opinions,*findings*, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. ...##
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Distance Approximation in Bounded-Degree and General Sparse Graphs
[chapter]

2006
*
Lecture Notes in Computer Science
*

Specifically, these properties are k-

doi:10.1007/11830924_43
fatcat:vvkdkhnkt5berjzrjnizsgskly
*edge**connectivity*,*subgraph*-freeness (*for*constant size*subgraphs*), being a Eulerian graph, and cycle-freeness. ... In this model the fraction of*edge*modifications is taken with respect to n*2*, and the*algorithm*may ask*for*the existence of an*edge*between any pair of vertices of its choice. ... A simple modification of our (non-sublinear time)*algorithm**for**approximating*the distance to*subgraph*freeness, yields A local*distributed**algorithm**for**approximating*the size of a minimum vertex cover ...
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