# An Improved Distributed Algorithm for Maximal Independent Set

@inproceedings{Ghaffari2016AnID, title={An Improved Distributed Algorithm for Maximal Independent Set}, author={Mohsen Ghaffari}, booktitle={SODA}, year={2016} }

The Maximal Independent Set (MIS) problem is one of the basics in the study of locality in distributed graph algorithms. This paper presents a very simple randomized algorithm for this problem providing a near-optimal local complexity, which incidentally, when combined with some known techniques, also leads to a near-optimal global complexity. Classical MIS algorithms of Luby [STOC'85] and Alon, Babai and Itai [JALG'86] provide the global complexity guarantee that, with high probability1, all…

## 170 Citations

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- Computer Science, MathematicsJ. Parallel Distributed Comput.
- 2019

Distributed Approximation of Maximum Independent Set and Maximum Matching

- Computer SciencePODC
- 2017

These algorithms are the first to achieve the provably optimal round complexity with respect to dependency on Δ and are part of a broad family of local aggregation algorithms for which a mechanism that allows the simulation to run in the CONGEST model without an additional overhead is described.

Distributed MIS via All-to-All Communication

- Computer SciencePODC
- 2017

An improved randomized distributed algorithm for congested clique model that improves quadratically on the O(log Δ) algorithm of [Ghaffari, SODA'16], and a certain local sparsification technique for MIS, which is of independent interest.

Tight Analysis of Parallel Randomized Greedy MIS

- Computer Science, MathematicsSODA
- 2018

A high probability upper bound of O(log n) on the round complexity of this algorithm in general graphs is proved, and it is shown that parallel randomized greedy MIS is as fast as the celebrated algorithm of Luby.

On the complexity of local distributed graph problems

- Computer Science, MathematicsSTOC
- 2017

The result can be viewed as showing that the only obstacle to getting efficient determinstic algorithms in the LOCAL model is an efficient algorithm to approximately round fractional values into integer values.

Tight Analysis of Parallel Randomized Greedy MIS

- Computer Science, MathematicsACM Trans. Algorithms
- 2020

A high probability upper bound of O(log n) on the round complexity of this algorithm in general graphs is proved and it is shown that parallel randomized greedy MIS is as fast as the celebrated algorithm of Luby.

Improved Distributed Lower Bounds for MIS and Bounded (Out-)Degree Dominating Sets in Trees

- Computer Science, MathematicsPODC
- 2021

This work proves lower bounds for a much more relaxed family of distributed symmetry breaking problems and provides a novel way to do simplifications for round elimination, which is expected to be of independent interest.

Distributed algorithms for the Lovász local lemma and graph coloring

- Computer Science, MathematicsPODC '14
- 2014

Two new distributed algorithms for the Lovasz Local Lemma (LLL) are provided that improve on both the efficiency and simplicity of the Moser-Tardos algorithm and prove that any distributed LLL algorithm requires Ω(log* n) rounds.

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- 2019

This paper presents a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank ƒ, and shows that integer covering-programs can be reduced to the Minimum Weight Set Cover problem in the distributed setting.

On Derandomizing Local Distributed Algorithms

- Mathematics2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
- 2018

This paper combines the method of conditional expectation with network decompositions to obtain a generic and clean recipe for derandomizing LOCAL algorithms, which leads to significant improvements on a number of problems, in cases resolving known open problems.

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