A fast and simple randomized parallel algorithm for maximal matching
Information Processing Letters
A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
Deterministic coin tossing with applications to optimal parallel list ranking
Information and Control
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Parallel symmetry-breaking in sparse graphs
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Locality in distributed graph algorithms
SIAM Journal on Computing
On the complexity of distributed network decomposition
Journal of Algorithms
A log-star distributed maximal independent set algorithm for growth-bounded graphs
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Distributed (δ+1)-coloring in linear (in δ) time
Proceedings of the forty-first annual ACM symposium on Theory of computing
Weak graph colorings: distributed algorithms and applications
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
An optimal bit complexity randomized distributed MIS algorithm (extended abstract)
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Stone age distributed computing
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Brief announcement: fair maximal independent sets in trees
Proceedings of the 2013 ACM symposium on Principles of distributed computing
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A maximal independent set on a graph is an inclusion-maximal set of mutually non-adjacent nodes. This basic symmetry breaking structure is vital for many distributed algorithms, which by now has been fueling the search for fast local algorithms to find such sets over several decades. In this paper, we present a solution with randomized running time O(√log n log log n) on trees, improving roughly quadratically on the state-of-the-art bound. Our algorithm is uniform and nodes need to exchange merely O(log n) many bits with high probability. In contrast to previous techniques achieving sublogarithmic running times, our approach does not rely on any bound on the number of independent neighbors (possibly with regard to an orientation of the edges).