(Note that all algorithms described in this paper exploit the buffer-packing and ‘‘fake’’ particle to eliminate inefficient
query communications.) Although it may seem counter intuitive to move a particle up to three times to appropriately relocate
it, the algorithm allows the number of communications to be exactly 2 d rather than the more precise two step method
described earlier which required a minimum of 3d 1 communications. The increase in message size is more than offset
by significant saving in latency due to fewer communications.