A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Locality in distributed graph algorithms
SIAM Journal on Computing
The distributed bit complexity of the ring: from the anonymous to the non-anonymous case
Information and Computation
SIAM Journal on Computing
Communication complexity
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Introduction to Distributed Algorithms
Introduction to Distributed Algorithms
Distributed Algorithms
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A fast parallel algorithm for the maximal independent set problem
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Maximal independent sets in radio networks
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
Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing)
Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing)
Bit complexity of breaking and achieving symmetry in chains and rings
Journal of the ACM (JACM)
Network decomposition and locality in distributed computation
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Refinement-based verification of local synchronization algorithms
FM'11 Proceedings of the 17th international conference on Formal methods
Beeping a maximal independent set
DISC'11 Proceedings of the 25th international conference on Distributed computing
Trading bit, message, and time complexity of distributed algorithms
DISC'11 Proceedings of the 25th international conference on Distributed computing
Efficient parallel and external matching
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
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We present a randomized distributed maximal independent set (MIS) algorithm for arbitrary graphs of size n that halts in time O(logn) with probability 1−o(n−1), each message containing 1 bit: thus its bit complexity per channel is O(logn) (the bit complexity is the number of bits we need to solve a distributed task, it measures the communication complexity). We assume that the graph is anonymous: unique identities are not available to distinguish the processes; we only assume that each vertex distinguishes between its neighbours by locally known channel names. Furthermore we do not assume that the size (or an upper bound on the size) of the graph is known. This algorithm is optimal (modulo a multiplicative constant) for the bit complexity and improves the best previous randomized distributed MIS algorithms (deduced from the randomized PRAM algorithm due to Luby [Lub86]) for general graphs which is O(log2n) per channel (it halts in time O(logn) and the size of each message is logn). This result is based on a powerful and general technique for converting unrealistic exchanges of messages containing real numbers drawn at random on each vertex of a network into exchanges of bits. Then we consider a natural question: what is the impact of a vertex inclusion in the MIS on distant vertices? We prove that this impact vanishes rapidly as the distance grows for bounded-degree vertices. We provide a counter-example that shows this result does not hold in general. We prove also that these results remain valid for Luby's algorithm presented by Lynch [Lyn96] and by Wattenhofer [Wat07]. This question remains open for the variant given by Peleg [Pel00].