Article

The price of being near-sighted

Authors:

Thomas Moscibroda,

Roger WattenhoferAuthors Info & Claims

SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm

Pages 980 - 989

Published: 22 January 2006 Publication History

Abstract

Achieving a global goal based on local information is challenging, especially in complex and large-scale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible trade-off between the amount of local information and the quality of the global solution for general covering and packing problems. Specifically, we give a distributed algorithm using only small messages which obtains an (ρΔ)^1/k-approximation for general covering and packing problems in time O(k²), where ρ depends on the LP's coefficients. If message size is unbounded, we present a second algorithm that achieves an O(n^1/k) approximation in O(k) rounds. Finally, we prove that these algorithms are close to optimal by giving a lower bound on the approximability of packing problems given that each node has to base its decision on information from its k-neighborhood.

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Cited By

Izumi TKitamura NNaruse TSchwartzman GAgrawal KLee I(2022)Fully Polynomial-Time Distributed Computation in Low-Treewidth GraphsProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538590(11-22)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538590
Abboud ACensor-Hillel KKhoury SPaz A(2021)Smaller Cuts, Higher Lower BoundsACM Transactions on Algorithms10.1145/346983417:4(1-40)Online publication date: 4-Oct-2021
https://dl.acm.org/doi/10.1145/3469834
Suomela J(2020)Using Round Elimination to Understand LocalityACM SIGACT News10.1145/3427361.342737451:3(63-81)Online publication date: 29-Sep-2020
https://dl.acm.org/doi/10.1145/3427361.3427374
Show More Cited By

Index Terms

The price of being near-sighted
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
  2. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
2. Theory of computation
  1. Design and analysis of algorithms

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Information & Contributors

Information

Published In

cover image ACM Conferences

SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm

January 2006

1261 pages

ISBN:0898716055

Sponsors

SIAM Activity Group on Discrete Mathematics
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

Society for Industrial and Applied Mathematics

United States

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Published: 22 January 2006

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

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Cited By

Izumi TKitamura NNaruse TSchwartzman GAgrawal KLee I(2022)Fully Polynomial-Time Distributed Computation in Low-Treewidth GraphsProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538590(11-22)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538590
Abboud ACensor-Hillel KKhoury SPaz A(2021)Smaller Cuts, Higher Lower BoundsACM Transactions on Algorithms10.1145/346983417:4(1-40)Online publication date: 4-Oct-2021
https://dl.acm.org/doi/10.1145/3469834
Suomela J(2020)Using Round Elimination to Understand LocalityACM SIGACT News10.1145/3427361.342737451:3(63-81)Online publication date: 29-Sep-2020
https://dl.acm.org/doi/10.1145/3427361.3427374
Deurer JKuhn FMaus YRobinson PEllen F(2019)Deterministic Distributed Dominating Set Approximation in the CONGEST ModelProceedings of the 2019 ACM Symposium on Principles of Distributed Computing10.1145/3293611.3331626(94-103)Online publication date: 16-Jul-2019
https://dl.acm.org/doi/10.1145/3293611.3331626
Ben Basat REven GKawarabayashi KSchwartzman GRobinson PEllen F(2019)Optimal Distributed Covering AlgorithmsProceedings of the 2019 ACM Symposium on Principles of Distributed Computing10.1145/3293611.3331577(104-106)Online publication date: 16-Jul-2019
https://dl.acm.org/doi/10.1145/3293611.3331577
Deng HZhao THou I(2019)Online Routing and Scheduling With Capacity Redundancy for Timely Delivery Guarantees in Multihop NetworksIEEE/ACM Transactions on Networking10.1109/TNET.2019.291739327:3(1258-1271)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1109/TNET.2019.2917393
Indyk PMahabadi SRubinfeld RVakilian AYodpinyanee ACzumaj A(2018)Set cover in sub-linear timeProceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3174304.3175463(2467-2486)Online publication date: 7-Jan-2018
https://dl.acm.org/doi/10.5555/3174304.3175463
Czumaj AŁącki JMądry AMitrović SOnak KSankowski PDiakonikolas IKempe DHenzinger M(2018)Round compression for parallel matching algorithmsProceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188764(471-484)Online publication date: 20-Jun-2018
https://dl.acm.org/doi/10.1145/3188745.3188764
Agarwal AChakaravarthy VChoudhury ARoy SSabharwal Y(2018)Set Cover Problems with Small Neighborhood CoversTheory of Computing Systems10.1007/s00224-017-9842-162:8(1763-1797)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.1007/s00224-017-9842-1
Mansour YPatt-Shamir BVardi S(2018)Constant-Time Local Computation AlgorithmsTheory of Computing Systems10.1007/s00224-017-9788-362:2(249-267)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1007/s00224-017-9788-3
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