  Motivated by a computer science algorithm known as `linear probing with
hashing' we study a new type of percolation model whose basic features include
a sequential `dropping' of particles on a substrate followed by their transport
via a `pushing' mechanism. Our exact solution in one dimension shows that,
unlike the ordinary random percolation model, the drop-push model has
nontrivial spatial correlations generated by the dynamics itself. The critical
exponents in the drop-push model are also different from that of the ordinary
percolation. The relevance of our results to computer science is pointed out.
