Brief Announcement: Using Read-k Inequalities to Analyze a Distributed MIS Algorithm

@article{Pemmaraju2016BriefAU,
  title={Brief Announcement: Using Read-k Inequalities to Analyze a Distributed MIS Algorithm},
  author={Sriram V. Pemmaraju and Talal Riaz},
  journal={Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing},
  year={2016}
}
  • S. Pemmaraju, Talal Riaz
  • Published 20 May 2016
  • Computer Science
  • Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing
Until recently, the fastest distributed MIS algorithm, even for simple graphs, e.g., unoriented trees, has been the simple randomized algorithm discovered in the 80s. This algorithm (commonly called Luby's algorithm) computes an MIS in O(log n) rounds (with high probability). This situation changed when Lenzen and Wattenhofer (PODC 2011) presented a randomized O(√log n} ⋅ log\log n)-round MIS algorithm for unoriented trees. This algorithm was improved by Barenboim et al. (FOCS 2012), resulting… 
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References

SHOWING 1-10 OF 18 REFERENCES
Using Read-k Inequalities to Analyze a Distributed MIS Algorithm
TLDR
The main thrust of this paper is the new probabilistic analysis via read-$k$ inequalities, for small values of $\alpha$, this algorithm is faster than the bounded arboricity MIS algorithm of Barenboim et al.
An Improved Distributed Algorithm for Maximal Independent Set
TLDR
A very simple randomized algorithm providing a near-optimal local complexity of O(log deg(v) + log 1/e) rounds, with probability at least 1, which incidentally, when combined with some known techniques, also leads to a near -optimal global complexity.
An optimal bit complexity randomized distributed MIS algorithm
We present a randomized distributed maximal independent set (MIS) algorithm for arbitrary graphs of size n that halts in time O(log n) with probability 1 − o(n−1), and only needs messages containing
Sublogarithmic distributed MIS algorithm for sparse graphs using Nash-Williams decomposition
TLDR
The first sublogarithmic algorithm for computing an MIS on graphs of bounded arboricity is devised, which demonstrates that this methodology is very powerful and shows nearly-tight lower bounds on the running time of any distributed algorithms for computing a forests-decomposition.
A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem
The Locality of Distributed Symmetry Breaking
TLDR
New bounds on the locality of several classical symmetry breaking tasks in distributed networks are presented and a new technique for reducing symmetry breaking problems on low arboricity graphs to low degree graphs is introduced.
MIS on trees
TLDR
This paper presents a solution with randomized running time O(√log n log log n) on trees, improving roughly quadratically on the state-of-the-art bound, and does not rely on any bound on the number of independent neighbors.
Deterministic Coin Tossing with Applications to Optimal Parallel List Ranking
A log-star distributed maximal independent set algorithm for growth-bounded graphs
TLDR
A novel distributed algorithm for the maximal independent set (MIS) problem that solves the connected dominating set problem for unit disk graphs in O(log* n) time, exponentially faster than the state-of-the-art algorithm.
A Fast and Simple Randomized Parallel Algorithm for Maximal Matching
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