Deterministic Low-Diameter Decompositions for Weighted Graphs and Distributed and Parallel Applications

This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one can also efficiently compute low-diameter decompositions. This...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Proceedings / annual Symposium on Foundations of Computer Science s. 1114 - 1121
Hlavní autori: Rozhon, Vaclav, Elkin, Michael, Grunau, Christoph, Haeupler, Bernhard
Médium: Konferenčný príspevok..
Jazyk:English
Vydavateľské údaje: IEEE 01.10.2022
Predmet:
Approximation algorithms
Clustering algorithms
Complexity theory
Computational modeling
Computer science
Distortion
Parallel algorithms
ISSN:2575-8454
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one can also efficiently compute low-diameter decompositions. This consequently implies solutions to many fundamental distance based problems using a polylogarithmic number of approximate distance computations.Our low-diameter decomposition generalizes and extends the line of work starting from [RG20] to weighted graphs in a very model-independent manner. Moreover, our clustering results have additional useful properties, including strong-diameter guarantees, separation properties, restricting cluster centers to specified terminals, and more. Applications include:-The first near-linear work and polylogarithmic depth randomized and deterministic parallel algorithm for low-stretch spanning trees (LSST) with polylogarithmic stretch. Previously, the best parallel LSST algorithm required m.n^{o(1)} work and n^{o(1)} depth and was inherently randomized. No deterministic LSST algorithm with truly sub-quadratic work and sub-linear depth was known.-The first near-linear work and polylogarithmic depth deterministic algorithm for computing an \ell_{1}-embedding into polylogarithmic dimensional space with polylogarithmic distortion. The best prior deterministic algorithms for \ell_{1}-embeddings either require large polynomial work or are inherently sequential.Even when we apply our techniques to the classical problem of computing a ball-carving with strong-diameter O(\log^{2}n) in an unweighted graph, our new clustering algorithm still leads to an improvement in round complexity from O(\log^{10}n) rounds [CG21] to O(\log^{4}n).
AbstractList This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one can also efficiently compute low-diameter decompositions. This consequently implies solutions to many fundamental distance based problems using a polylogarithmic number of approximate distance computations.Our low-diameter decomposition generalizes and extends the line of work starting from [RG20] to weighted graphs in a very model-independent manner. Moreover, our clustering results have additional useful properties, including strong-diameter guarantees, separation properties, restricting cluster centers to specified terminals, and more. Applications include:-The first near-linear work and polylogarithmic depth randomized and deterministic parallel algorithm for low-stretch spanning trees (LSST) with polylogarithmic stretch. Previously, the best parallel LSST algorithm required m.n^{o(1)} work and n^{o(1)} depth and was inherently randomized. No deterministic LSST algorithm with truly sub-quadratic work and sub-linear depth was known.-The first near-linear work and polylogarithmic depth deterministic algorithm for computing an \ell_{1}-embedding into polylogarithmic dimensional space with polylogarithmic distortion. The best prior deterministic algorithms for \ell_{1}-embeddings either require large polynomial work or are inherently sequential.Even when we apply our techniques to the classical problem of computing a ball-carving with strong-diameter O(\log^{2}n) in an unweighted graph, our new clustering algorithm still leads to an improvement in round complexity from O(\log^{10}n) rounds [CG21] to O(\log^{4}n).
Author Elkin, Michael
Rozhon, Vaclav
Haeupler, Bernhard
Grunau, Christoph
Author_xml – sequence: 1
  givenname: Vaclav
  surname: Rozhon
  fullname: Rozhon, Vaclav
  email: rozhonv@inf.ethz.ch
  organization: ETH Zurich
– sequence: 2
  givenname: Michael
  surname: Elkin
  fullname: Elkin, Michael
  email: elkinm@cs.bgu.ac.il
  organization: Ben-Gurion University of the Negev
– sequence: 3
  givenname: Christoph
  surname: Grunau
  fullname: Grunau, Christoph
  email: cgrunau@inf.ethz.ch
  organization: ETH Zurich
– sequence: 4
  givenname: Bernhard
  surname: Haeupler
  fullname: Haeupler, Bernhard
  email: bernhard.haeupler@inf.ethz.ch
  organization: ETH Zurich & Carnegie Mellon University
BookMark eNotj9tKAzEURaMo2Fa_QB_yA1Nzn8lj6dgqFCqo-FhOMmfayNxIRsS_t1WfNnvB2rCn5KLrOyTkjrM558zer7bLF62UzueCCTFnjLP8jEy5MVppza0-JxOhc50VSqsrMk3pgzHFNFMTsi9xxNiGLqQxeLrpv7IyQHuCtETft0Ofwhj6LtG6j_Qdw_4wYkXXEYZDotBVtDyqMbjPEz71Z4jQNNjQxTA0wcOvfU0ua2gS3vznjLytHl6Xj9lmu35aLjZZEEyOGRQFSADQonLgaq80cGGZ8cZ5KGr03Aj0hTC5lVBVTubW1TKv0B6_OmnkjNz-7QZE3A0xtBC_d9ZaYwoufwD2ZFs5
CODEN IEEPAD
ContentType Conference Proceeding
DBID 6IE
6IH
CBEJK
RIE
RIO
DOI 10.1109/FOCS54457.2022.00107
DatabaseName IEEE Electronic Library (IEL) Conference Proceedings
IEEE Proceedings Order Plan (POP) 1998-present by volume
IEEE Xplore All Conference Proceedings
IEEE Xplore
IEEE Proceedings Order Plans (POP) 1998-present
DatabaseTitleList
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Xplore
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
Computer Science
EISBN 1665455195
9781665455190
EISSN 2575-8454
EndPage 1121
ExternalDocumentID 9996681
Genre orig-research
GrantInformation_xml – fundername: European Research Council
  funderid: 10.13039/501100000781
GroupedDBID --Z
29O
6IE
6IH
6IK
ALMA_UNASSIGNED_HOLDINGS
CBEJK
RIE
RIO
ID FETCH-LOGICAL-i203t-a88a3aaa52dbabfc45a12906c6bca8fec162ec826793addb379bf37de9654b363
IEDL.DBID RIE
ISICitedReferencesCount 7
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000909382900101&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
IngestDate Wed Aug 27 02:53:24 EDT 2025
IsPeerReviewed false
IsScholarly true
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-i203t-a88a3aaa52dbabfc45a12906c6bca8fec162ec826793addb379bf37de9654b363
PageCount 8
ParticipantIDs ieee_primary_9996681
PublicationCentury 2000
PublicationDate 2022-Oct.
PublicationDateYYYYMMDD 2022-10-01
PublicationDate_xml – month: 10
  year: 2022
  text: 2022-Oct.
PublicationDecade 2020
PublicationTitle Proceedings / annual Symposium on Foundations of Computer Science
PublicationTitleAbbrev FOCS
PublicationYear 2022
Publisher IEEE
Publisher_xml – name: IEEE
SSID ssj0040504
Score 2.3258078
Snippet This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can...
SourceID ieee
SourceType Publisher
StartPage 1114
SubjectTerms Approximation algorithms
Clustering algorithms
Complexity theory
Computational modeling
Computer science
Distortion
Parallel algorithms
Title Deterministic Low-Diameter Decompositions for Weighted Graphs and Distributed and Parallel Applications
URI https://ieeexplore.ieee.org/document/9996681
WOSCitedRecordID wos000909382900101&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED6VigGWQlvEWx4YCU3iJE5G1FAYSqnEq1vlxwVVghb1AX8fn5sWkFjYklss-WT78_m77wM444nxAyVJDy9DL1JINi-ce1GBETcCU-7s2566otdLB4OsX4HzdS8MIjryGV7Qp3vLNxO9oFJZy4Fz6rPeECJZ9mqtdl2LO_yobI0L_KzVuWvfk86MsFfAkDQ5A_-3gYo7Pzq1_428A83vRjzWXx8xu1DBcR1qKycGVi7MOmzfrtVXZw14yUuOixNhZt3Jp5eP5BsFWY5EIl8xtZiFrOzZVUfRsGsSr54xOTYsJz1dssKyYfrvyymZrryyyx8P3k147Fw9tG-80lDBG4U-n3syTSWXUsahUVIVOoollaESnSgt0wJ1kISo7YXDLlq77ykuMlVwYTBL4kjxhO9BdTwZ4z6wOLbIwFgwYUIdodIqiAuRqswmW0gLeg6gQbM4fF9qZgzLCTz8O3wEW5SmJUnuGKrz6QJPYFN_zEez6alL9Bcr66zI
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8JAEJ4QNVEvKGB8uwePVtpun0dDRYwFSUTlRvYxNSQKhof-fXdKQU28eGvnsslOdvfb2W--D-CcB9p2pCA9vBgtTyLZvHBueRl6XIcY8dy-7SkNO52o34-7JbhY9cIgYk4-w0v6zN_y9VjNqVRWz8E59Vmvk3NW0a213HcN8rC9ojnOseN6877xQEozobkEuqTK6di_LVTyE6RZ_t_YO1D7bsVj3dUhswslHFWgvPRiYMXSrMB2e6W_Oq3CS1KwXHIZZpaOP61kKN4oyBIkGvmSq8UMaGXPeX0UNbsh-eopEyPNElLUJTMsE6b_rpiQ7coru_rx5F2Dx-Z1r9GyCksFa-jafGaJKBJcCOG7WgqZKc8XVIgKVCCViDJUTuCiMlcOs2zNzid5GMuMhxrjwPckD_gerI3GI9wH5vsGG2gDJ7SrPJRKOn4WRjI26Q6FgT0HUKVZHLwvVDMGxQQe_h0-g81Wr50O0tvO3RFsUcoWlLljWJtN5ngCG-pjNpxOTvOkfwFVmLAR
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=proceeding&rft.title=Proceedings+%2F+annual+Symposium+on+Foundations+of+Computer+Science&rft.atitle=Deterministic+Low-Diameter+Decompositions+for+Weighted+Graphs+and+Distributed+and+Parallel+Applications&rft.au=Rozhon%2C+Vaclav&rft.au=Elkin%2C+Michael&rft.au=Grunau%2C+Christoph&rft.au=Haeupler%2C+Bernhard&rft.date=2022-10-01&rft.pub=IEEE&rft.eissn=2575-8454&rft.spage=1114&rft.epage=1121&rft_id=info:doi/10.1109%2FFOCS54457.2022.00107&rft.externalDocID=9996681