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Massively Parallel Algorithms for Distance Approximation and Spanners [article]

Amartya Shankha Biswas, Michal Dory, Mohsen Ghaffari, Slobodan Mitrović, Yasamin Nazari
2021 arXiv   pre-print
By now, we have quite fast algorithms – usually sublogarithmic-time and often poly(loglog n)-time, or even faster – for a number of fundamental graph problems in the massively parallel computation (MPC  ...  To the best of our knowledge, this is the first sublogarithmic-time MPC algorithm for distance approximations.  ...  Acknowledgements We thank Merav Parter, Michael Dinitz and Aditya Krishnan for fruitful discussions. AS. Biswas is supported by MIT-IBM Watson AI Lab and research collaboration agreement No.  ... 
arXiv:2003.01254v5 fatcat:m57k7kkv2vhnjj7ltzc6qehnre

Brief Announcement: Massively Parallel Approximate Distance Sketches

Michael Dinitz, Yasamin Nazari, Michael Wagner
2019 International Symposium on Distributed Computing  
We initiate their study in newer (and arguably more realistic) models of distributed computation: the Congested Clique model and the Massively Parallel Computation (MPC) model.  ...  This result has additional applications such as the first polylogarithmic time algorithm for constant approximate single-source shortest paths for weighted graphs in the low memory MPC setting.  ...  In MPC, we can go even further and compute slightly suboptimal sketches in time that is only polylogarithmic. 42:2 Massively Parallel Approximate Distance Sketches Distance Oracles and Sketches.  ... 
doi:10.4230/lipics.disc.2019.42 dblp:conf/wdag/DinitzN19 fatcat:3xjwtruhrvfbllwl5lwflt4pcu

t-Spanners for metric space searching

Gonzalo Navarro, Rodrigo Paredes, Edgar Chávez
2007 Data & Knowledge Engineering  
Our key idea is to regard the t-spanner as an approximation to the complete graph of distances among the objects, and to use it as a compact device to simulate the large matrix of distances required by  ...  For this sake, several t-spanner construction, updating, and search algorithms are proposed and experimentally evaluated. We show that our technique is competitive against current approaches.  ...  For shortness we have called the optimized basic algorithm t-Spanner 1, the massive edge-insertion algorithm t-Spanner 2, the incremental algorithm t-Spanner 3, the recursive algorithm t-Spanner 4, and  ... 
doi:10.1016/j.datak.2007.05.002 fatcat:t73cdcgftjcnvnuawrnxcb35ne

Massively Parallel Approximate Distance Sketches

Michael Dinitz, Yasamin Nazari, Michael Wagner
2020 International Conference on Principles of Distributed Systems  
ACM Subject Classification Theory of computation → Massively parallel algorithms of network communication (depending on the precise model).  ...  Thus after this preprocessing, anyone who is interested in analyzing the massive graph has access to approximate distances essentially for free, making this a powerful tool for distributed graph analytics  ...  : 35:4 Massively Parallel Approximate Distance Sketches Theorem 1.  ... 
doi:10.4230/lipics.opodis.2019.35 dblp:conf/opodis/DinitzN19 fatcat:kiajlm5pirc4hfrd3w7wvtmfi4

Efficient algorithms for constructing (1+∊,β)-spanners in the distributed and streaming models

Michael Elkin, Jian Zhang
2005 Distributed computing  
We also show that any streaming algorithm for o(n)-approximate distance computation requires Ω(n) bits of space.  ...  We also show that our protocol for constructing (1 + , β)spanners can be adapted to the streaming model, and devise a streaming algorithm that uses a constant number of passes and O(n 1+1/κ · log n) bits  ...  Acknowledgment: The authors are very grateful to Joan Feigenbaum for inspiring and stimulating discussions, helpful comments, and remarks.  ... 
doi:10.1007/s00446-005-0147-2 fatcat:nurcpl2dtvf3jkjyqjpyem5qdy

Massively Parallel Approximate Distance Sketches [article]

Michael Dinitz, Yasamin Nazari
2019 arXiv   pre-print
We initiate their study in newer (and arguably more realistic) models of distributed computation: the Congested Clique model and the Massively Parallel Computation (MPC) model.  ...  This result has additional applications such as the first polylogarithmic time algorithm for constant approximate single-source shortest paths for weighted graphs in the low memory MPC setting.  ...  Note that unlike centralized Bellman-Ford nodes do not store and initial distance estimate (due to space limitation in the streaming model). This algorithm uses O(|S| · nh) total space.  ... 
arXiv:1810.09027v4 fatcat:o6yztntpxbg27onobkvirnw4rq

Algorithm Engineering (Dagstuhl Seminar 13391)

Andrew V. Goldberg, Giuseppe F. Italiano, David S. Johnson, Dorothea Wagner, Marc Herbstritt
2014 Dagstuhl Reports  
Algorithm engineering touches other research areas such as algorithm theory, combinatorial optimization, computer architecture, parallel and distributed computing, high-performance computing, and operations  ...  All these topics are driven by the need for efficient algorithms and libraries for problems that appear frequently in real-world applications.  ...  -Algorithm Engineering the work of the aggregate operator's processing steps. We provide an extensive study of the properties of the proposed aggregate operators and the new data structures.  ... 
doi:10.4230/dagrep.3.9.169 dblp:journals/dagstuhl-reports/GoldbergIJW13 fatcat:n75s6d7obngxbitr4rcxxadmxq

On Graph Problems in a Semi-streaming Model [chapter]

Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, Jian Zhang
2004 Lecture Notes in Computer Science  
In the course of this general study, we give semi-streaming constant approximation algorithms for the unweighted and weighted matching problems, along with a further algorithm improvement for the bipartite  ...  We also exhibit log n/ log log n semistreaming approximations to the diameter and the problem of computing the distance between specified vertices in a weighted graph.  ...  Particularly, the efficiency of an algorithm in the semi-streaming model is measured by S(m, n), P (m, n) and T (m, n) as in definition 2.  ... 
doi:10.1007/978-3-540-27836-8_46 fatcat:irtqu3gw7zhmdlofoltgyq53dm

On graph problems in a semi-streaming model

Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, Jian Zhang
2005 Theoretical Computer Science  
In the course of this general study, we give semi-streaming constant approximation algorithms for the unweighted and weighted matching problems, along with a further algorithm improvement for the bipartite  ...  We also exhibit log n/ log log n semistreaming approximations to the diameter and the problem of computing the distance between specified vertices in a weighted graph.  ...  Particularly, the efficiency of an algorithm in the semi-streaming model is measured by S(m, n), P (m, n) and T (m, n) as in definition 2.  ... 
doi:10.1016/j.tcs.2005.09.013 fatcat:am5i2stnv5h4bjmazgkzbfohsu

Distribution-Sensitive Construction of the Greedy Spanner [article]

Sander P. A. Alewijnse, Quirijn W. Bouts, Alex P. ten Brink, Kevin Buchin
2014 arXiv   pre-print
This characterization gives a O(n log^2 n log^2 log n) expected time bound on our greedy spanner algorithm, making it the first subquadratic time algorithm for this problem on any interesting class of  ...  time algorithm for this problem that does not make assumptions on E.  ...  These 'approximations' have few edges compared to the complete graph, while approximately maintaining distances, making them a useful tool in many areas.  ... 
arXiv:1401.1085v2 fatcat:hxn5liy2mreopafq6rajm6lhny

Graph sketches

Kook Jin Ahn, Sudipto Guha, Andrew McGregor
2012 Proceedings of the 31st symposium on Principles of Database Systems - PODS '12  
Finally, for distance estimation we present sketchbased spanner constructions.  ...  The non-adaptive sketches, such as those for sparsification and subgraphs, give us single-pass algorithms for distributed data streams with insertion and deletions.  ...  Acknowledgments We thank Graham Cormode, Atri Rudra, and David Woodruff for helpful discussions.  ... 
doi:10.1145/2213556.2213560 dblp:conf/pods/AhnGM12 fatcat:3xaqt3j5lvhy7koj2vlvvlncaq

Distribution-Sensitive Construction of the Greedy Spanner [chapter]

Sander P. A. Alewijnse, Quirijn W. Bouts, Alex P. Ten Brink
2014 Lecture Notes in Computer Science  
We propose a novel algorithm design which uses the observation that for many point sets, the greedy spanner has many 'short' edges that can be determined locally and usually quickly.  ...  E is a t-spanner, making it the first subquadratic time algorithm for this problem that does not make assumptions on E.  ...  reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/978-3-662-44777-2_6 fatcat:qk4ri5nfwbbg7gk7qlkfc2w7da

Distribution-Sensitive Construction of the Greedy Spanner

Sander P. A. Alewijnse, Quirijn W. Bouts, Alex P. ten Brink, Kevin Buchin
2016 Algorithmica  
We propose a novel algorithm design which uses the observation that for many point sets, the greedy spanner has many 'short' edges that can be determined locally and usually quickly.  ...  E is a t-spanner, making it the first subquadratic time algorithm for this problem that does not make assumptions on E.  ...  reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s00453-016-0160-9 fatcat:mkppxbd5dfc37f46x6uswc3pru

(1+ϵ)-Approximate Shortest Paths in Dynamic Streams [article]

Michael Elkin, Chhaya Trehan
2021 arXiv   pre-print
Currently existing solutions for this problem either build a sparse multiplicative spanner of the input graph and compute shortest paths in the spanner offline, or compute an exact single source BFS tree  ...  In this paper we show that (1+ϵ)-approximate single-source shortest paths can be computed in this setting with Õ(n^1+1/κ) space using just constantly many passes in unweighted graphs, and polylogarithmically  ...  Most of the algorithms for computing (approximate) distances and shortest paths in the streaming setting compute a sparse spanner, and then employ it for computing exact shortest paths and distances in  ... 
arXiv:2107.13309v1 fatcat:ogfmdw5tyrgkrlehl3usptqbp4

Graph Distances in the Data-Stream Model

Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, Jian Zhang
2009 SIAM journal on computing (Print)  
(3) Graph-distance lower bounds: Any t-approximation of the distance between two nodes requires Ω(n 1+1/t ) space.  ...  We are motivated by both the practical challenge of processing massive graphs such as the web graph and the desire for a better theoretical understanding of the datastream model.  ...  We thank Martin Sauerhoff for helpful comments on the results in section 4 and the anonymous referees for their comments on the presentation.  ... 
doi:10.1137/070683155 fatcat:uz3437bdh5bkpidj4zzd6vy4r4
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