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Information and Control
Locality in distributed graph algorithms
SIAM Journal on Computing
Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases
IEEE Transactions on Parallel and Distributed Systems
On the distributed complexity of computing maximal matchings
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Leader Election Problem on Networks in which Processor Identity Numbers Are Not Distinct
IEEE Transactions on Parallel and Distributed Systems
On the Distributed Complexity of Computing Maximal Matchings
SIAM Journal on Discrete Mathematics
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STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
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Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Some simple distributed algorithms for sparse networks
Distributed Computing
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SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the complexity of distributed graph coloring
Proceedings of the twenty-fifth annual 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
Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Lower bounds for local approximation
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
ACM Computing Surveys (CSUR)
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Lower bounds for local approximation
Journal of the ACM (JACM)
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We study distributed algorithms that find a maximal matching in an anonymous, edge-coloured graph. If the edges are properly coloured with k colours, there is a trivial greedy algorithm that finds a maximal matching in k-1 synchronous communication rounds. The present work shows that the greedy algorithm is optimal in the general case: if A is a deterministic distributed algorithm that finds a maximal matching in anonymous, k-edge-coloured graphs, then there is a worst-case input in which the running time of A is at least k1 rounds. If we focus on graphs of maximum degree Δ, it is known that a maximal matching can be found in O(Δ+ log* k) rounds, and prior work implies a lower bound of Ω(polylog(Δ) + log* k) rounds. Our work closes the gap between upper and lower bounds: the complexity is Θ(Δ+ log* k) rounds. To our knowledge, this is the first linear-in-Δ lower bound for the distributed complexity of a classical graph problem.