research-article

Local Computation: Lower and Upper Bounds

Authors:

Thomas Moscibroda, and

Roger WattenhoferAuthors Info & Claims

Journal of the ACM (JACM), Volume 63, Issue 2

Article No.: 17, Pages 1 - 44

https://doi.org/10.1145/2742012

Published: 31 March 2016 Publication History

Abstract

The question of what can be computed, and how efficiently, is at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a distributed fashion. More precisely, if nodes of a network must base their decision on information in their local neighborhood only, how well can they compute or approximate a global (optimization) problem? In this paper we give the first polylogarithmic lower bound on such local computation for (optimization) problems including minimum vertex cover, minimum (connected) dominating set, maximum matching, maximal independent set, and maximal matching. In addition, we present a new distributed algorithm for solving general covering and packing linear programs. For some problems this algorithm is tight with the lower bounds, whereas for others it is a distributed approximation scheme. Together, our lower and upper bounds establish the local computability and approximability of a large class of problems, characterizing how much local information is required to solve these tasks.

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Index Terms

Local Computation: Lower and Upper Bounds
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Network flows
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows
  2. Randomness, geometry and discrete structures

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 63, Issue 2

May 2016

249 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/2906142

Editor:
Éva Tardos
Cornell University

Issue’s Table of Contents

Copyright © 2016 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 31 March 2016

Accepted: 01 January 2015

Revised: 01 December 2014

Received: 01 November 2011

Published in JACM Volume 63, Issue 2

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Assadi SKonrad CNaidu KSundaresan JMohar BShinkar IO'Donnell R(2024)O(log log n) Passes Is Optimal for Semi-streaming Maximal Independent SetProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649763(847-858)Online publication date: 10-Jun-2024
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Assadi SKol GZhang Z(2024)Rounds vs. Communication Tradeoffs for Maximal Independent SetsSIAM Journal on Computing10.1137/22M1536972(FOCS22-20-FOCS22-59)Online publication date: 25-Mar-2024
https://doi.org/10.1137/22M1536972
Chang Y(2024)The energy complexity of diameter and minimum cut computation in bounded-genus networksTheoretical Computer Science10.1016/j.tcs.2023.114279982(114279)Online publication date: Jan-2024
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Halldórsson MRawitz D(2024)Distributed Fractional Local Ratio and Independent Set ApproximationStructural Information and Communication Complexity10.1007/978-3-031-60603-8_16(281-299)Online publication date: 23-May-2024
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