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Algebraic Methods in the Congested Clique
[article]

2015
*
arXiv
*
pre-print

*In*this work, we use

*algebraic*

*methods*for studying distance computation and subgraph detection tasks

*in*

*the*

*congested*

*clique*model. ...

*In*conjunction with known techniques from centralised algorithmics, this gives significant improvements over previous best upper bounds

*in*

*the*

*congested*

*clique*model. ... Conclusions

*In*this work, we demonstrate that

*algebraic*

*methods*-especially fast matrix multiplication -can be used to design efficient algorithms

*in*

*the*

*congested*

*clique*model, resulting

*in*algorithms ...

##
###
Algebraic Methods in the Congested Clique

2015
*
Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing - PODC '15
*

*In*this work, we use

*algebraic*

*methods*for studying distance computation and subgraph detection tasks

*in*

*the*

*congested*

*clique*model. ...

*In*conjunction with known techniques from centralised algorithmics, this gives significant improvements over previous best upper bounds

*in*

*the*

*congested*

*clique*model. ... Conclusions

*In*this work, we demonstrate that

*algebraic*

*methods*-especially fast matrix multiplication -can be used to design efficient algorithms

*in*

*the*

*congested*

*clique*model, resulting

*in*algorithms ...

##
###
Algebraic methods in the congested clique

2016
*
Distributed computing
*

*In*this work, we use

*algebraic*

*methods*for studying distance computation and subgraph detection tasks

*in*

*the*

*congested*

*clique*model. ...

*In*conjunction with known techniques from centralised algorithmics, this gives significant improvements over previous best upper bounds

*in*

*the*

*congested*

*clique*model. ... Conclusions

*In*this work, we demonstrate that

*algebraic*

*methods*-especially fast matrix multiplication -can be used to design efficient algorithms

*in*

*the*

*congested*

*clique*model, resulting

*in*algorithms ...

##
###
Further Algebraic Algorithms in the Congested Clique Model and Applications to Graph-Theoretic Problems
[article]

2016
*
arXiv
*
pre-print

[PODC'15] recently showed how to efficiently implement centralized

arXiv:1608.02674v1
fatcat:fruxbgqsfrb43db3q65xpo7trm
*algebraic*algorithms for matrix multiplication*in**the**congested**clique*model, a model of distributed computing that has received increasing ... As applications of these techniques, we obtain more efficient algorithms for*the*computation, again*in**the**congested**clique*model, of*the*all-pairs shortest paths and*the*diameter*in*directed and undirected ... This work is supported by*the*Grant-*in*-Aid for Young Scientists (A) No. 16H05853,*the*Grant-*in*-Aid for Scientific Research (A) No. 16H01705, and*the*Grant-*in*-Aid for Scientific Research on Innovative Areas ...##
###
The Laplacian Paradigm in the Broadcast Congested Clique

2022
*
Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing
*

*In*this paper, we bring

*the*main tools of

*the*Laplacian paradigm to

*the*Broadcast

*Congested*

*Clique*. ... We show how to solve certain linear programs up to additive error 𝜖 with 𝑛 constraints on an 𝑛-vertex Broadcast

*Congested*

*Clique*network

*in*O( √ 𝑛 log(1/𝜖)) rounds. ... This project has received funding from

*the*European Research Council (ERC) under

*the*European Union's Horizon 2020 research and innovation programme (grant agreement No 947702). ...

##
###
Interpolative Boolean algebra based multicriteria routing algorithm

2015
*
Yugoslav Journal of Operations Research
*

*In*order to improve quality-of-service of distributed applications, we propose a multi-criteria algorithm based on interpolative Boolean

*algebra*for routing

*in*an overlay network.We use a mesh topology ...

*The*proposed routing algorithm determines

*the*path by using interpolative Boolean

*algebra*, which satisfies quality-of-service requirements. ... A

*clique*is a subset of a graph such that every two nodes

*in*

*the*subset are connected by a link, and from

*the*above, it gives p Q , as

*the*set of

*the*maximal

*cliques*containing only links on p . ...

##
###
Joint congestion control

2005
*
Proceedings of the 8th ACM international symposium on Modeling, analysis and simulation of wireless and mobile systems - MSWiM '05
*

*In*this paper we present a model for

*the*joint

*congestion*control, routing and MAC link access for ad hoc wireless networks. ...

*The*resulting algorithm directly translates into a distributed cross-layer scheme for joint

*congestion*control, routing and link scheduling of

*the*wireless links which revolves around link layer pricing ...

*In*order to compute (30) and (31) all nodes need to find out which

*cliques*they belong to and all rates of

*the*links

*in*these

*cliques*. ...

##
###
Sparse matrix multiplication and triangle listing in the Congested Clique model

2019
*
Theoretical Computer Science
*

There is a deterministic algorithm that computes

doi:10.1016/j.tcs.2019.11.006
fatcat:pxvorrbw2vdf3kfjnydk74h7me
*the*number of 4-cycles*in*an n-node graph G*in*O(m 2/3 /n + 1) rounds*in**the**Congested**Clique*model, where m is*the*number of edges of G. ... We show how to multiply two n × n matrices S and T over semirings*in**the**Congested**Clique*model, where n nodes communicate*in*a fully connected synchronous network using O(log n)bit messages, within O( ... Related graph computations*in**the**Congested**Clique*model: Triangle counting*in**the**Congested**Clique*model was addressed by Dolev et al. ...##
###
The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian

1999
*
Combinatorics, probability & computing
*

We show that

doi:10.1017/s0963548399003958
fatcat:uun5sb5aqbbflfa44wzvx7zr7m
*the*best bounds this*method*can produce for*clique*cmbeddings are*the*same as for a related*method*that uses*clique*cmbcddings and edge lengths to produce bounds. ...*In*both*methods*,*the*multiplier shows up*in**the*bound.*The*two*methods*are duals of each other*in**the*following sense: THEOREM 4.3. ...##
###
Derandomizing Local Distributed Algorithms under Bandwidth Restrictions
[article]

2016
*
arXiv
*
pre-print

On

arXiv:1608.01689v1
fatcat:twz26utvfbh2petsftqjxdhg2q
*the*way to obtaining*the*above, we show that*in**the**Congested**Clique*model, which allows all-to-all communication, there is a deterministic MIS algorithm that runs*in*O(Δ n) rounds.*the*maximum degree ... For*the**CONGEST*model,*the*only known previous solution is a coloring-based O(Δ + ^* n)-round algorithm, where Δ is*the*maximal degree*in**the*graph. ... Acknowledgments: We are very grateful to Mohsen Ghaffari for many helpful discussions and useful observations involving*the*derandomization of his MIS algorithm. ...##
###
Quantum Distributed Algorithms for Detection of Cliques
[article]

2022
*
arXiv
*
pre-print

Moreover, we show a circuit-complexity barrier on proving a lower bound of

arXiv:2201.03000v1
fatcat:ghufv72hdrdn5fuacvisdltuae
*the*form Ω(n^3/5+ϵ) for K_p-detection for any p ≥ 4, even*in**the*classical (non-quantum) distributed*CONGEST*setting. ...*In*this paper we present a framework for fast quantum distributed*clique*detection. ...*Congest*model and*the**Congested**Clique*model. ...##
###
Sublinear-Time Distributed Algorithms for Detecting Small Cliques and Even Cycles

2019
*
International Symposium on Distributed Computing
*

*In*this paper we give sublinear-time distributed algorithms

*in*

*the*

*CONGEST*model for subgraph detection for two classes of graphs:

*cliques*and even-length cycles. ... We show for

*the*first time that all copies of 4-

*cliques*and 5-

*cliques*

*in*

*the*network graph can be listed

*in*sublinear time, O(n 5/6+o(1) ) rounds and O(n 21/22+o(1) ) rounds, respectively. ...

*In*

*the*

*Congested*

*Clique*, an O(n 0.158 ) round algorithm for C k -detection was shown by [4] based on

*algebraic*

*methods*. ...

##
###
Lower Bounds for Induced Cycle Detection in Distributed Computing
[article]

2021
*
arXiv
*
pre-print

*In*

*the*standard

*CONGEST*model of distributed computing,

*the*complexity of

*clique*/cycle detection and listing has received a lot of attention recently. ... We first show a Ω̃(n) lower bound for detecting

*the*existence of an induced k-cycle for any k≥ 4

*in*

*the*

*CONGEST*model. ...

*In*

*the*

*CONGESTED*

*CLIQUE*model, for any constant k ≥ 3, k-cycle can be detected

*in*O(2 O(k) n 0.158 ) rounds by an

*algebraic*algorithm which uses

*the*matrix multiplication [6] and for k ≥ 2, 2k-cycle ...

##
###
Sparse Matrix Multiplication and Triangle Listing in the Congested Clique Model
[article]

2019
*
arXiv
*
pre-print

We multiply two n × n matrices S,T over semirings

arXiv:1802.04789v4
fatcat:tmvmycoeorh3lckwtzeybki4fu
*in**the**Congested**Clique*model, where n fully connected nodes communicate synchronously using O( n)-bit messages, within O(nz(S)^1/3 nz(T)^1/3/n + 1) rounds ... Our algorithmic contribution is a new deterministic*method*of restructuring*the*input matrices*in*a sparsity-aware manner, which assigns each node with element-wise multiplication tasks that are not necessarily ... O(1) rounds*in**the**Congested**Clique*model. ...##
###
The Laplacian Paradigm in the Broadcast Congested Clique
[article]

2022
*
arXiv
*
pre-print

*In*this paper, we bring

*the*main tools of

*the*Laplacian paradigm to

*the*Broadcast

*Congested*

*Clique*. ... We show how to solve certain linear programs up to additive error ϵ with n constraints on an n-vertex Broadcast

*Congested*

*Clique*network

*in*Õ(√(n)log(1/ϵ)) rounds. ... This project has received funding from

*the*European Research Council (ERC) under

*the*European Union's Horizon 2020 research and innovation programme (grant agreement No 947702). ...

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