A linear time algorithm for routing over the cells is presented. The a
lgorithm tries to reduce maximum channel density by routing some conne
ctions over the cells. The algorithm first defines a new scheme for ch
annel representation and formulates the problem based on an intersecti
on graph derived from the new scheme. Then, a feasible independent set
of the intersection graph is found for routing some subnets over the
cells. The algorithm is implemented and evaluated with several well kn
own benchmarks, In comparison with previous research, our results are
satisfactory, and the algorithm takes substantially less CPU time than
those of previous works. For Deutsch's difficult example, the previou
s algorithms lake about 29.25 seconds on an average but our new algori
thm needs only 5.6 seconds.