Electronic Design Automation

11.5.2. Quadratic techniques

In quadratic placement techniques, the placement problem is transformed into a sequence of convex quadratic programs. Convex quadratic program is a mathematical program with a convex and quadratic objective function and linear constraints.

11.5.2.1. Quadratic wirelength

First, the way to express the placement cost function as a quadratic function is presented. Suppose for the time being that all nets in the circuit are 2-pin nets. (Multi-pin nets will be discussed later.) Consider a net {i, j} (i.e., connecting module i and module j). Its wirelength is given by the Manhattan distance between the modules:This is ...