  The kd-tree is a fundamental tool in computer science. Among others, an
application of the kd-tree search (oct-tree method) to fast evaluation of
particle interactions and neighbor search is highly important since
computational complexity of these problems are reduced from O(N^2) with a brute
force method to O(N log N) with the tree method where N is a number of
particles. In this paper, we present a parallel implementation of the tree
method running on a graphic processor unit (GPU). We successfully run a
simulation of structure formation in the universe very efficiently. On our
system, which costs roughly $900, the run with N ~ 2.87x10^6 particles took
5.79 hours and executed 1.2x10^13 force evaluations in total. We obtained the
sustained computing speed of 21.8 Gflops and the cost per Gflops of 41.6/Gflops
that is two and half times better than the previous record in 2006.
