## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, September 27, 2018, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Jara Uitto

## Sparsifying Distributed Algorithms in the Low-Memory Massively Parallel Computation Model

The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale parallel computation frameworks and has recently gained a lot of importance, especially in the context of classic graph problems. Unfortunately, most of the known efficient MPC algorithms seem to get fundamentally stuck at the linear-memory barrier: their efficiency crucially relies on each machine having space at least linear in the number n of nodes. As this might not only be prohibitively large, but also allows for easy if not trivial solutions for sparse graphs, we are interested in the low-memory MPC model, where the space per machine is restricted to be strongly sublinear, that is, n^d for any 0 < d < 1. We study maximal matching (MM) and maximal independent set (MIS) and introduce a method for "sparsifying" distributed algorithms that, roughly speaking, allows us to run local distributed algorithms without the knowledge of the whole local topology. This, in turn, allows us to speed up the local algorithms using the global communication power of the MPC model without breaking the memory restrictions. In the case of MIS and MM, our method yields algorithms with runtime of O( sqrt(log Delta) ), where Delta is the maximum degree of the input graph. As a by-product, we obtain a 2-approximation for Minimum Vertex Cover, (2 + eps)-approximation for maximum weighted matching, and a (1 + eps)-approximation for maximum cardinality matching without a loss in the overall runtimes.

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