  The problem of counting collisions or interactions is common in areas as
computer graphics and scientific simulations. Since it is a major bottleneck in
applications of these areas, a lot of research has been carried out on such
subject, mainly focused on techniques that allow calculations to be performed
within pruned sets of objects. This paper focuses on how interaction
calculation (such as collisions) within these sets can be done more efficiently
than existing approaches. Two algorithms are proposed: a sequential algorithm
that has linear complexity at the cost of high memory usage; and a parallel
algorithm, mathematically proved to be correct, that manages to use GPU
resources more efficiently than existing approaches. The proposed and existing
algorithms were implemented, and experiments show a speedup of 21.7 for the
sequential algorithm (on small problem size), and 1.12 for the parallel
proposal (large problem size). By improving interaction calculation, this work
contributes to research areas that promote interconnection in the modern world,
such as computer graphics and robotics.
