Lower and Upper Bounds for Distributed Packing and Covering

We make a step towards understanding the distributed complexity of global optimization problems. We give bounds on the trade-off between locality and achievable approximation ratio of distributed algorithms for packing and covering problems. We show that in k communication rounds, maximum matching and therefore packing problems cannot be approximated better than Ω(n 2 /k) and Ω(∆/k) where c is a small constant and n and ∆ denote the number of nodes and the maximum degree of the network graph, respectively. This means that

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