Computing the Maximum Overlap of Two Convex Polygons under Translations

Abstract.

Finding a vast array of applications, the list-ranking problem has emerged as one of the fundamental techniques in parallel algorithm design. Surprisingly, the best previously known algorithm to rank a list of n items on a reconfigurable mesh of size $n \times n$ was running in O(log n ) time. It was open for more than 8 years to obtain a faster algorithm for this important problem.

Our main contribution is to provide the first breakthrough: we propose a deterministic list-ranking algorithm that runs in O(log^* n ) time as well as a randomized one running in O(1) expected time, both on a reconfigurable mesh of size $n \times n$ . Our results open the door to a large number of efficient list-ranking-based algorithms on reconfigurable meshes.