In this paper, 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 Gong, Liu, and Preas (1990). They stated the complexity of this problem to be unknown, and presented a min {1,k/d(S)} 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(kn/sup 2/) dynamic programming algorithm for the TRMPS problem, where n is the number of nets. We also present a parallel version of our algorithm, which has a complexity of O(kn). Our algorithm can also be extended to solve the TRMPS problem, in the presence of prerouted 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(kn/sup 2/) time.

In this paper we solve the planar over-the-cell routing problem, in which nets must have at least one terminal on the boundary. Such nets allow for nontraditional cell designs, where all terminals must be placed on the boundaries giving a degree of freedom to the cell designer. We present a dynamic programming algorithm that optimally solves this problem, in O(K/sup 2/n/sup 4/) time, where K is the number of tracks available over the cell for a given cell row region, and n is the number of nets to be routed.

Several Ov er-the-Cell (OTC) routing algorithms have been proposed for two and three layer processes.All the existing OTC routers can be used only on the cell models for whic h they were developed for.In this paper, we develop a uni ed approach t o m ulti-layer routing, motiv ated by o v er-the-cell routing, which can be used for full-custom la youts.Our approac h can also be directly applied to standard cell layouts, irrespective of the cell model used in the design.Our router has been implemen ted in C and tested on industrial benchmarks, suc h as PRIMARY I and PRIMARY I I , for which it obtained channel-less layouts.

The Two Row Maximum Planar Subset (TRMPS) problem asks for finding the maximum planar subset of nets, that can be routed between two rows of terminals an a cell row. This problem was first encountered by Gong, Liu, and Preas (1990). They declared it open, and presented an approximation algorithm for this problem. In this paper we show that TRMPS problem can be solved optimally in polynomial time, and we present an O(kn/sup 2/) algorithm to solve this problem. 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 an improved approximation algorithm, for over the cell routing in middle terminal model standard cell layouts.>

In this paper, we present an hierarchical clock routing scheme, which minimizes the longest source to sink path, and obtains a path balanced clock tree with minimal total wirelength. Our scheme takes into consideration, the hierarchical design of a circuit. Our approach is applicable to large VLSI circuits and MCM's. The algorithm has been implemented and experimental results are encouraging.>

Several Over-the-Cell (OTC) routing algorithms have been proposed for two and three layer processes. All the existing OTC routers assume that the terminals are laid out in a specific predetermined fashion. These restrictions on the terminals complicate the task of cell design and increase the width of the cells. In this paper, we develop a four layer OTC router which allows arbitrary terminal locations. Freed from fixed terminal placement restrictions, cell designers can aim to design with minimum width. Our router has been implemented and tested on several circuits. For most of the circuits, it obtained channel-less layouts.>