research-article

Networks cannot compute their diameter in sublinear time

Authors:

Silvio Frischknecht,

Stephan Holzer,

Roger WattenhoferAuthors Info & Claims

SODA '12: Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms

Pages 1150 - 1162

Published: 17 January 2012 Publication History

Abstract

We study the problem of computing the diameter of a network in a distributed way. The model of distributed computation we consider is: in each synchronous round, each node can transmit a different (but short) message to each of its neighbors. We provide an Ω(n) lower bound for the number of communication rounds needed, where n denotes the number of nodes in the network. This lower bound is valid even if the diameter of the network is a small constant. We also show that a (3/2 − ε)-approximation of the diameter requires Ω (√n + D) rounds. Furthermore we use our new technique to prove an Ω (√n + D) lower bound on approximating the girth of a graph by a factor 2 − ε.

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Cited By

Magniez FNayak A(2022)Quantum Distributed Complexity of Set Disjointness on a LineACM Transactions on Computation Theory10.1145/351275114:1(1-22)Online publication date: 4-Mar-2022
https://dl.acm.org/doi/10.1145/3512751
Elkin M(2020)Distributed Exact Shortest Paths in Sublinear TimeJournal of the ACM10.1145/338716167:3(1-36)Online publication date: 18-May-2020
https://dl.acm.org/doi/10.1145/3387161
Daga MHenzinger MNanongkai DSaranurak TCharikar MCohen E(2019)Distributed edge connectivity in sublinear timeProceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing10.1145/3313276.3316346(343-354)Online publication date: 23-Jun-2019
https://dl.acm.org/doi/10.1145/3313276.3316346
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Index Terms

Networks cannot compute their diameter in sublinear time
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Network flows
2. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows

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cover image ACM Other conferences

SODA '12: Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms

January 2012

1764 pages

Sponsors

Kyoto University: Kyoto University

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 17 January 2012

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SODA '12

Sponsor:

Kyoto University

SODA '12: ACM-SIAM Symposium on Discrete Algorithms

January 17 - 19, 2012

Kyoto, Japan

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Cited By

Magniez FNayak A(2022)Quantum Distributed Complexity of Set Disjointness on a LineACM Transactions on Computation Theory10.1145/351275114:1(1-22)Online publication date: 4-Mar-2022
https://dl.acm.org/doi/10.1145/3512751
Elkin M(2020)Distributed Exact Shortest Paths in Sublinear TimeJournal of the ACM10.1145/338716167:3(1-36)Online publication date: 18-May-2020
https://dl.acm.org/doi/10.1145/3387161
Daga MHenzinger MNanongkai DSaranurak TCharikar MCohen E(2019)Distributed edge connectivity in sublinear timeProceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing10.1145/3313276.3316346(343-354)Online publication date: 23-Jun-2019
https://dl.acm.org/doi/10.1145/3313276.3316346
Kerenidis IRosén AUrrutia F(2019)Multi-Party Protocols, Information Complexity and PrivacyACM Transactions on Computation Theory10.1145/331323011:2(1-29)Online publication date: 17-Mar-2019
https://dl.acm.org/doi/10.1145/3313230
Hoang LPontecorvi MDathathri RGill GYou BPingali KRamachandran VHollingsworth JKeidar I(2019)A round-efficient distributed betweenness centrality algorithmProceedings of the 24th Symposium on Principles and Practice of Parallel Programming10.1145/3293883.3295729(272-286)Online publication date: 16-Feb-2019
https://dl.acm.org/doi/10.1145/3293883.3295729
Izumi TLe Gall FRobinson PEllen F(2019)Quantum Distributed Algorithm for the All-Pairs Shortest Path Problem in the CONGEST-CLIQUE ModelProceedings of the 2019 ACM Symposium on Principles of Distributed Computing10.1145/3293611.3331628(84-93)Online publication date: 16-Jul-2019
https://dl.acm.org/doi/10.1145/3293611.3331628
Bacrach NCensor-Hillel KDory MEfron YLeitersdorf DPaz ARobinson PEllen F(2019)Hardness of Distributed OptimizationProceedings of the 2019 ACM Symposium on Principles of Distributed Computing10.1145/3293611.3331597(238-247)Online publication date: 16-Jul-2019
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Foerster KKorhonen JRybicki JSchmid SRobinson PEllen F(2019)Does Preprocessing Help under Congestion?Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing10.1145/3293611.3331581(259-261)Online publication date: 16-Jul-2019
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Saikia PKarmakar SHansdah RKrishnaswamy DVaidya N(2019)A simple 2(1-1/l) factor distributed approximation algorithm for steiner tree in the CONGEST modelProceedings of the 20th International Conference on Distributed Computing and Networking10.1145/3288599.3288629(41-50)Online publication date: 4-Jan-2019
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Lenzen CPatt-Shamir BPeleg D(2019)Distributed distance computation and routing with small messagesDistributed Computing10.1007/s00446-018-0326-632:2(133-157)Online publication date: 1-Apr-2019
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