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Algebraic Methods in the Congested Clique [article]

Keren Censor-Hillel, Petteri Kaski, Janne H. Korhonen, Christoph Lenzen, Ami Paz, Jukka Suomela
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  ... 
arXiv:1503.04963v1 fatcat:y4cplbnngfcabfeml2rtzd4bzu

Algebraic Methods in the Congested Clique

Keren Censor-Hillel, Petteri Kaski, Janne H. Korhonen, Christoph Lenzen, Ami Paz, Jukka Suomela
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  ... 
doi:10.1145/2767386.2767414 dblp:conf/podc/Censor-HillelKK15 fatcat:gcbzzqjeovfxxlxtf4jmxnfedy

Algebraic methods in the congested clique

Keren Censor-Hillel, Petteri Kaski, Janne H. Korhonen, Christoph Lenzen, Ami Paz, Jukka Suomela
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  ... 
doi:10.1007/s00446-016-0270-2 fatcat:cyod5vphmzb75ahytcoqw5wjsi

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

François Le Gall
2016 arXiv   pre-print
[PODC'15] recently showed how to efficiently implement centralized 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  ... 
arXiv:1608.02674v1 fatcat:fruxbgqsfrb43db3q65xpo7trm

The Laplacian Paradigm in the Broadcast Congested Clique

Sebastian Forster, Tijn de Vos
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).  ... 
doi:10.1145/3519270.3538436 fatcat:jmv4ojwqxrcx7gnendq2ppi5ce

Interpolative Boolean algebra based multicriteria routing algorithm

Marina Jeremic, Aleksandar Rakicevic, Ivana Dragovic
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 .  ... 
doi:10.2298/yjor140430029j fatcat:knudxqgdqrcjfikx5h6sb2yyq4

Joint congestion control

Francesco Lo Presti
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.  ... 
doi:10.1145/1089444.1089497 dblp:conf/mswim/Presti05 fatcat:kpewhyxu2rhupfd32mrzh76m44

Sparse matrix multiplication and triangle listing in the Congested Clique model

Keren Censor-Hillel, Dean Leitersdorf, Elia Turner
2019 Theoretical Computer Science  
There is a deterministic algorithm that computes 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.  ... 
doi:10.1016/j.tcs.2019.11.006 fatcat:pxvorrbw2vdf3kfjnydk74h7me

The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian

S. GUATTERY, T. LEIGHTON, G. L. MILLER
1999 Combinatorics, probability & computing  
We show that 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.  ... 
doi:10.1017/s0963548399003958 fatcat:uun5sb5aqbbflfa44wzvx7zr7m

Derandomizing Local Distributed Algorithms under Bandwidth Restrictions [article]

Keren Censor-Hillel, Merav Parter, Gregory Schwartzman
2016 arXiv   pre-print
On 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.  ... 
arXiv:1608.01689v1 fatcat:twz26utvfbh2petsftqjxdhg2q

Quantum Distributed Algorithms for Detection of Cliques [article]

Keren Censor-Hillel, Orr Fischer, François Le Gall, Dean Leitersdorf, Rotem Oshman
2022 arXiv   pre-print
Moreover, we show a circuit-complexity barrier on proving a lower bound of 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.  ... 
arXiv:2201.03000v1 fatcat:ghufv72hdrdn5fuacvisdltuae

Sublinear-Time Distributed Algorithms for Detecting Small Cliques and Even Cycles

Talya Eden, Nimrod Fiat, Orr Fischer, Fabian Kuhn, Rotem Oshman, Michael Wagner
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.  ... 
doi:10.4230/lipics.disc.2019.15 dblp:conf/wdag/EdenFFKO19 fatcat:7fz7jidenvfvxmqnzxgusbhzq4

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

François Le Gall, Masayuki Miyamoto
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  ... 
arXiv:2110.00741v1 fatcat:xa6saob2tbhixngmv6i2s3uexi

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

Keren Censor-Hillel, Dean Leitersdorf, Elia Turner
2019 arXiv   pre-print
We multiply two n × n matrices S,T over semirings 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.  ... 
arXiv:1802.04789v4 fatcat:tmvmycoeorh3lckwtzeybki4fu

The Laplacian Paradigm in the Broadcast Congested Clique [article]

Sebastian Forster, Tijn de Vos
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).  ... 
arXiv:2205.12059v1 fatcat:3xjoivu74fffhoanqo32cweac4
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