&&ReWrAp:HEADERFOOTER:0:ReWrAp&&

Date of Award

2009

Degree Type

Thesis

Degree Name

Master of Applied Science (MASc)

Department

Computational Engineering and Science

Supervisor

Tamás Terlaky

Co-Supervisor

Antoine Deza

Language

English

Abstract

The global routing problem is becoming more and more important in the design of today's integrated circuits. A small chip may contain up to millions of components and wires. Although global routing can be formulated as an integer linear programming problem, it is hard to solve directly using currently available solvers. We discuss a relaxation of the problem to a linear programming (LP) formulation with a fractional solution. However, the relaxation yields an NP-hard problem. In this thesis, we introduce three relaxations: the primal (Pc), the Lagrange dual (Dc), and the unimodular (PI) formulation. At optimality, all three problems have the same objective value. A new way to tackle the LP problem is introduced: first solve the Dc and try to find Lagrange multipliers in order to build the PI model, from which an integer solution can be obtained directly. An implementation based on the discussed approaches was tested using IBM benchmarks.

McMaster University Library