Date of Award


Degree Name

Master of Science


Computer Science

First Advisor

Dr. Naveed A. Sherwani

Second Advisor

Dr. Ajay Gupta

Third Advisor

Dr. Alfred Boals

Access Setting

Masters Thesis-Open Access


Planar over the cell routing in standard cell layouts is an important problem and it has been studied quite extensively. In two layer standard cell design methodology, Ml layer is typically used for connections internal to the cell, and the M2 layer is available for routing over-the-cell. In this thesis, we consider the Two Row Maximum Planar Subset (TRMPS) problem in Over-The-Cell routing. The TRMPS problem requires selection of the maximum planar subset of nets, which can be routed between two rows of terminals in a cell row. This problem was first encountered by Cong, Liu, and Preas [3]. They stated the complexity of this problem to be unknown, and presented a min{1, } approximation algorithm, where k is the number of tracks available over the cell area and d(S) is the density of a solution S.

We show that TRMPS problem can be solved optimally in polynomial time. We present a O(kn2 ) dynamic programming algorithm for the TRMPS problem, where n is the number of nets. Our algorithm can also be extended to solve the TRMPS problem, in the presence of pre-routed nets, a chosen subset of nets, as well as for planar channel routing. We also apply our technique to obtain a 0.5 approximation, for over the cell routing in middle terminal model, thus improving the best known existing algorithm. The weighted version of the TRMPS problem, as well as, all the extensions can also be solved in O(kn2) time.