Tight Bounds for a Distributed Selection Game with Applications to Fixed-Connection Machines

We deene a distributed selection game that generalizes a selection problem considered by Kosaraju 7]. We ooer a tight analysis of our distributed selection game, and show that the lower bound for this abstract communication game directly implies near-tight lower bounds for certain selection problems on xed-connection machines. For example, we prove that any deterministic comparison-based selection algorithm on an (n= logn)-processor bounded-degree hypercubic machine requires (log 3=2 n) steps in the worst case. This lower bound implies a non-trivial separation between the power of bounded-degree hy-percubic and expander-based machines. Furthermore , we show that the algorithm underlying our tight upper bound for the distributed selection game can be adapted to run in O((log 3=2 n) (loglog n) 2) steps on any (n= logn)-processor hypercubic machine.