Distributed algorithms for random graphs

In this article we study statistical properties of a commonly used network model - an Erd?s-Renyi random graph G ( n , p ) . We are interested in the performance of distributed algorithms on large networks, which might be represented by G ( n , p ) . We concentrate on classical problems from the field of distributed algorithms such as: finding a maximal independent set, a vertex colouring, an approximation of a minimum dominating set, a maximal matching, an edge colouring and an approximation of a maximum matching. We propose new algorithms, which with probability close to one as n ? ∞ construct anticipated structures in G ( n , p ) in a low number of rounds. Moreover, in some cases, we modify known algorithms to obtain better efficiency on G ( n , p ) .

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