Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space

The Massively Parallel Computation (MPC) model is an emerging that distills core aspects of distributed and parallel computation, developed as a tool to solve combinatorial (typically graph) problems in systems many machines with limited space. Recent work has focused on the regime which have sublinear (in n , number nodes input space, randomized algorithms presented for fundamental Maximal Matching Independent Set. However, there been no prior corresponding deterministic algorithms. A major challenge underlying space setting local each machine might be too small store all edges incident single node. This poses considerable obstacle compared classical models node assumed know easy access its edges. To overcome this barrier, we introduce new graph sparsification technique deterministically computes low-degree subgraph, additional property solving problem subgraph provides significant progress towards original graph. Using framework derandomize well-known algorithm Luby [SICOMP’86], obtain O (log ? + log )-round MPC Set ( ? ) any constant > 0. These also run ?) rounds closely related CONGESTED CLIQUE, improving upon state-of-the-art bound 2 by Censor-Hillel et al. [DISC’17].