# On Lower Bounds for the Time and the Bit Complexity of some Probabilistic Distributed Graph Algorithms

Abstract : This paper concerns probabilistic distributed graph algorithms to solve classical graph problems such as colouring, maximal matching or maximal independent set. We consider anonymous networks (no unique identifiers are available) where vertices communicate by single bit messages. We present a general framework, based on coverings, for proving lower bounds for the bit complexity and thus the execution time to solve these problems. In this way we obtain new proofs of some well known results and some new ones. The last part gives impossibility results on the existence of Las Vegas distributed algorithms to break symmetries at distance $k$ for $k\geq 3.$

https://hal.archives-ouvertes.fr/hal-00873468
Contributor : Yves Métivier <>
Submitted on : Tuesday, October 15, 2013 - 4:31:03 PM
Last modification on : Wednesday, May 23, 2018 - 9:12:01 PM

### Identifiers

• HAL Id : hal-00873468, version 1

### Citation

Allyx Fontaine, Yves Métivier, John Michael Robson, Akka Zemmari. On Lower Bounds for the Time and the Bit Complexity of some Probabilistic Distributed Graph Algorithms. 40th International Conference on Current Trends in Theory and Practice of Computer Science, Jan 2014, Slovakia. pp.235-245. ⟨hal-00873468⟩

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