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
SIAM Journal on Discrete Mathematics
Locality in distributed graph algorithms
SIAM Journal on Computing
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
On the complexity of distributed network decomposition
Journal of Algorithms
Efficient computation of implicit representations of sparse graphs
Discrete Applied Mathematics
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Extremal Graph Theory
Efficient leader election using sense of direction
Distributed Computing
On the locality of bounded growth
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
On the complexity of distributed graph coloring
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Graph Treewidth and Geometric Thickness Parameters
Discrete & Computational Geometry
A randomized distributed algorithm for the maximal independent set problem in growth-bounded graphs
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Network decomposition and locality in distributed computation
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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 coloring in Õ (√log n) Bit Rounds
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Fast deterministic distributed maximal independent set computation on growth-bounded graphs
DISC'05 Proceedings of the 19th international conference on 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
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
A new technique for distributed symmetry breaking
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Deterministic distributed vertex coloring in polylogarithmic time
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Distributed graph coloring in a few rounds
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Distributed deterministic edge coloring using bounded neighborhood independence
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Deterministic Distributed Vertex Coloring in Polylogarithmic Time
Journal of the ACM (JACM)
Distributed coloring depending on the chromatic number or the neighborhood growth
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Combinatorial algorithms for distributed graph coloring
DISC'11 Proceedings of the 25th international conference on Distributed computing
On the locality of some NP-complete problems
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Symmetry breaking depending on the chromatic number or the neighborhood growth
Theoretical Computer Science
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We study the distributed maximal independent set (henceforth, MIS) problem on sparse graphs. Currently, there are known algorithms with a sublogarithmic running time for this problem on oriented trees and graphs of bounded degrees. We devise the first sublogarithmic algorithm for computing MIS on graphs of bounded arboricity. This is a large family of graphs that includes graphs of bounded degree, planar graphs, graphs of bounded genus, graphs of bounded treewidth, graphs that exclude a fixed minor, and many other graphs. We also devise efficient algorithms for coloring graphs from these families. These results are achieved by the following technique that may be of independent interest. Our algorithm starts with computing a certain graph-theoretic structure, called Nash-Williams forests-decomposition. Then this structure is used to compute the MIS or coloring. Our results demonstrate that this methodology is very powerful. Finally, we show nearly-tight lower bounds on the running time of any distributed algorithm for computing a forests-decomposition.