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Massively Parallel Algorithms for Distance Approximation and Spanners
[article]

2021
*
arXiv
*
pre-print

By now, we have quite fast

arXiv:2003.01254v5
fatcat:m57k7kkv2vhnjj7ltzc6qehnre
*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. ...##
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Brief Announcement: Massively Parallel Approximate Distance Sketches

2019
*
International Symposium on Distributed Computing
*

We initiate their study in newer (

doi:10.4230/lipics.disc.2019.42
dblp:conf/wdag/DinitzN19
fatcat:3xjwtruhrvfbllwl5lwflt4pcu
*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. ...##
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t-Spanners for metric space searching

2007
*
Data & Knowledge Engineering
*

Our key idea is to regard the t-

doi:10.1016/j.datak.2007.05.002
fatcat:t73cdcgftjcnvnuawrnxcb35ne
*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*...##
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Massively Parallel Approximate Distance Sketches

2020
*
International Conference on Principles of Distributed Systems
*

ACM Subject Classification Theory of computation →

doi:10.4230/lipics.opodis.2019.35
dblp:conf/opodis/DinitzN19
fatcat:kiajlm5pirc4hfrd3w7wvtmfi4
*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. ...##
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Efficient algorithms for constructing (1+∊,β)-spanners in the distributed and streaming models

2005
*
Distributed computing
*

We also show that any streaming

doi:10.1007/s00446-005-0147-2
fatcat:nurcpl2dtvf3jkjyqjpyem5qdy
*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. ...##
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Massively Parallel Approximate Distance Sketches
[article]

2019
*
arXiv
*
pre-print

We initiate their study in newer (

arXiv:1810.09027v4
fatcat:o6yztntpxbg27onobkvirnw4rq
*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. ...##
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Algorithm Engineering (Dagstuhl Seminar 13391)

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. ...

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

2004
*
Lecture Notes in Computer Science
*

In the course of this general study, we give semi-streaming constant

doi:10.1007/978-3-540-27836-8_46
fatcat:irtqu3gw7zhmdlofoltgyq53dm
*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. ...##
###
On graph problems in a semi-streaming model

2005
*
Theoretical Computer Science
*

In the course of this general study, we give semi-streaming constant

doi:10.1016/j.tcs.2005.09.013
fatcat:am5i2stnv5h4bjmazgkzbfohsu
*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. ...##
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Distribution-Sensitive Construction of the Greedy Spanner
[article]

2014
*
arXiv
*
pre-print

This characterization gives a O(n log^2 n log^2 log n) expected time bound on our greedy

arXiv:1401.1085v2
fatcat:hxn5liy2mreopafq6rajm6lhny
*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. ...##
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Graph sketches

2012
*
Proceedings of the 31st symposium on Principles of Database Systems - PODS '12
*

Finally,

doi:10.1145/2213556.2213560
dblp:conf/pods/AhnGM12
fatcat:3xaqt3j5lvhy7koj2vlvvlncaq
*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. ...##
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Distribution-Sensitive Construction of the Greedy Spanner
[chapter]

2014
*
Lecture Notes in Computer Science
*

We propose a novel

doi:10.1007/978-3-662-44777-2_6
fatcat:qk4ri5nfwbbg7gk7qlkfc2w7da
*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. ...##
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Distribution-Sensitive Construction of the Greedy Spanner

2016
*
Algorithmica
*

We propose a novel

doi:10.1007/s00453-016-0160-9
fatcat:mkppxbd5dfc37f46x6uswc3pru
*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. ...##
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(1+ϵ)-Approximate Shortest Paths in Dynamic Streams
[article]

2021
*
arXiv
*
pre-print

Currently existing solutions

arXiv:2107.13309v1
fatcat:ogfmdw5tyrgkrlehl3usptqbp4
*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 ...##
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Graph Distances in the Data-Stream Model

2009
*
SIAM journal on computing (Print)
*

(3) Graph-

doi:10.1137/070683155
fatcat:uz3437bdh5bkpidj4zzd6vy4r4
*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. ...
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