Academic Journal
View in EDS

The Message Complexity of Distributed Graph Optimization

Bibliographic Details
Title: The Message Complexity of Distributed Graph Optimization
Authors: Dufoulon, Fabien, Pai, Shreyas, Pandurangan, Gopal, Pemmaraju, Sriram V., Robinson, Peter
Contributors: Fabien Dufoulon and Shreyas Pai and Gopal Pandurangan and Sriram V. Pemmaraju and Peter Robinson
Publisher Information: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Publication Year: 2024
Collection: DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics )
Subject Terms: Distributed graph algorithm, message complexity, distributed approximation
Description: The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization problems. We focus on four classical graph optimization problems: Maximum Matching (MaxM), Minimum Vertex Cover (MVC), Minimum Dominating Set (MDS), and Maximum Independent Set (MaxIS). In the sequential setting, these problems are representative of a wide spectrum of hardness of approximation. While there has been some progress in understanding the round complexity of distributed algorithms (for both exact and approximate versions) for these problems, much less is known about their message complexity and its relation with the quality of approximation. We almost fully quantify the message complexity of distributed graph optimization by showing the following results: 1) Cubic regime: Our first main contribution is showing essentially cubic, i.e., Ω̃(n³) lower bounds (where n is the number of nodes in the graph) on the message complexity of distributed exact computation of Minimum Vertex Cover (MVC), Minimum Dominating Set (MDS), and Maximum Independent Set (MaxIS). Our lower bounds apply to any distributed algorithm that runs in polynomial number of rounds (a mild and necessary restriction). Our result is significant since, to the best of our knowledge, this are the first ω(m) (where m is the number of edges in the graph) message lower bound known for distributed computation of such classical graph optimization problems. Our bounds are essentially tight, as all these problems can be solved trivially using O(n³) messages in polynomial rounds. All these bounds hold in the standard CONGEST model of distributed computation in which messages are of O(log n) size. 2) Quadratic regime: In contrast, we show that if we allow approximate computation then Θ̃(n²) messages are both necessary and sufficient. Specifically, we show that Ω̃(n²) messages are required for constant-factor ...
Document Type: article in journal/newspaper
conference object
File Description: application/pdf
Language: English
Relation: Is Part Of LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.41
DOI: 10.4230/LIPIcs.ITCS.2024.41
Availability: https://doi.org/10.4230/LIPIcs.ITCS.2024.41
https://nbn-resolving.org/urn:nbn:de:0030-drops-195690
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.41
Rights: https://creativecommons.org/licenses/by/4.0/legalcode
Accession Number: edsbas.A475EEF
Database: BASE
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://doi.org/10.4230/LIPIcs.ITCS.2024.41#
    Name: EDS - BASE (ns324271)
    Category: fullText
    Text: View record from BASE
Header DbId: edsbas
DbLabel: BASE
An: edsbas.A475EEF
RelevancyScore: 965
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 964.707946777344
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: The Message Complexity of Distributed Graph Optimization
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Dufoulon%2C+Fabien%22">Dufoulon, Fabien</searchLink><br /><searchLink fieldCode="AR" term="%22Pai%2C+Shreyas%22">Pai, Shreyas</searchLink><br /><searchLink fieldCode="AR" term="%22Pandurangan%2C+Gopal%22">Pandurangan, Gopal</searchLink><br /><searchLink fieldCode="AR" term="%22Pemmaraju%2C+Sriram+V%2E%22">Pemmaraju, Sriram V.</searchLink><br /><searchLink fieldCode="AR" term="%22Robinson%2C+Peter%22">Robinson, Peter</searchLink>
– Name: Author
  Label: Contributors
  Group: Au
  Data: Fabien Dufoulon and Shreyas Pai and Gopal Pandurangan and Sriram V. Pemmaraju and Peter Robinson
– Name: Publisher
  Label: Publisher Information
  Group: PubInfo
  Data: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2024
– Name: Subset
  Label: Collection
  Group: HoldingsInfo
  Data: DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics )
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Distributed+graph+algorithm%22">Distributed graph algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22message+complexity%22">message complexity</searchLink><br /><searchLink fieldCode="DE" term="%22distributed+approximation%22">distributed approximation</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization problems. We focus on four classical graph optimization problems: Maximum Matching (MaxM), Minimum Vertex Cover (MVC), Minimum Dominating Set (MDS), and Maximum Independent Set (MaxIS). In the sequential setting, these problems are representative of a wide spectrum of hardness of approximation. While there has been some progress in understanding the round complexity of distributed algorithms (for both exact and approximate versions) for these problems, much less is known about their message complexity and its relation with the quality of approximation. We almost fully quantify the message complexity of distributed graph optimization by showing the following results: 1) Cubic regime: Our first main contribution is showing essentially cubic, i.e., Ω̃(n³) lower bounds (where n is the number of nodes in the graph) on the message complexity of distributed exact computation of Minimum Vertex Cover (MVC), Minimum Dominating Set (MDS), and Maximum Independent Set (MaxIS). Our lower bounds apply to any distributed algorithm that runs in polynomial number of rounds (a mild and necessary restriction). Our result is significant since, to the best of our knowledge, this are the first ω(m) (where m is the number of edges in the graph) message lower bound known for distributed computation of such classical graph optimization problems. Our bounds are essentially tight, as all these problems can be solved trivially using O(n³) messages in polynomial rounds. All these bounds hold in the standard CONGEST model of distributed computation in which messages are of O(log n) size. 2) Quadratic regime: In contrast, we show that if we allow approximate computation then Θ̃(n²) messages are both necessary and sufficient. Specifically, we show that Ω̃(n²) messages are required for constant-factor ...
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: article in journal/newspaper<br />conference object
– Name: Format
  Label: File Description
  Group: SrcInfo
  Data: application/pdf
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: NoteTitleSource
  Label: Relation
  Group: SrcInfo
  Data: Is Part Of LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.41
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.4230/LIPIcs.ITCS.2024.41
– Name: URL
  Label: Availability
  Group: URL
  Data: https://doi.org/10.4230/LIPIcs.ITCS.2024.41<br />https://nbn-resolving.org/urn:nbn:de:0030-drops-195690<br />https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.41
– Name: Copyright
  Label: Rights
  Group: Cpyrght
  Data: https://creativecommons.org/licenses/by/4.0/legalcode
– Name: AN
  Label: Accession Number
  Group: ID
  Data: edsbas.A475EEF
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.A475EEF
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.4230/LIPIcs.ITCS.2024.41
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: Distributed graph algorithm
        Type: general
      – SubjectFull: message complexity
        Type: general
      – SubjectFull: distributed approximation
        Type: general
    Titles:
      – TitleFull: The Message Complexity of Distributed Graph Optimization
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Dufoulon, Fabien
      – PersonEntity:
          Name:
            NameFull: Pai, Shreyas
      – PersonEntity:
          Name:
            NameFull: Pandurangan, Gopal
      – PersonEntity:
          Name:
            NameFull: Pemmaraju, Sriram V.
      – PersonEntity:
          Name:
            NameFull: Robinson, Peter
      – PersonEntity:
          Name:
            NameFull: Fabien Dufoulon and Shreyas Pai and Gopal Pandurangan and Sriram V. Pemmaraju and Peter Robinson
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2024
          Identifiers:
            – Type: issn-locals
              Value: edsbas
            – Type: issn-locals
              Value: edsbas.oa
ResultId 1