research-article

Fully dynamic maximal independent set with sublinear update time

Authors:

Krzysztof Onak,

Baruch Schieber,

Shay SolomonAuthors Info & Claims

STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing

Pages 815 - 826

https://doi.org/10.1145/3188745.3188922

Published: 20 June 2018 Publication History

Abstract

A maximal independent set (MIS) can be maintained in an evolving m-edge graph by simply recomputing it from scratch in O(m) time after each update. But can it be maintained in time sublinear in m in fully dynamic graphs?

We answer this fundamental open question in the affirmative. We present a deterministic algorithm with amortized update time O(min{Δ,m^3/4}), where Δ is a fixed bound on the maximum degree in the graph and m is the (dynamically changing) number of edges.

We further present a distributed implementation of our algorithm with O(min{Δ,m^3/4}) amortized message complexity, and O(1) amortized round complexity and adjustment complexity (the number of vertices that change their output after each update). This strengthens a similar result by Censor-Hillel, Haramaty, and Karnin (PODC’16) that required an assumption of a non-adaptive oblivious adversary.

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Index Terms

Fully dynamic maximal independent set with sublinear update time
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Dynamic graph algorithms

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cover image ACM Conferences

STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing

June 2018

1332 pages

ISBN:9781450355599

DOI:10.1145/3188745

General Chairs:
Ilias Diakonikolas
University of Southern California, USA
,
David Kempe
University of Southern California, USA
,
Program Chair:
Monika Henzinger
University of Vienna, Austria

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Published: 20 June 2018

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https://dl.acm.org/doi/10.1145/3662158.3662794
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
https://dl.acm.org/doi/10.1145/3618260.3649763
Tan YZhou JRong XDu MQi C(2024)Efficient computation of maximum weighted independent sets on weighted dynamic graphThe Journal of Supercomputing10.1007/s11227-023-05841-980:8(10418-10443)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1007/s11227-023-05841-9
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