UNIMODULARITY IN SOLVING ILP MODELS OF THE GLOBAL ROUTING PROBLEM

Abstract

<p>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 (<em>Pc</em>), the Lagrange dual (<em>Dc</em>), and the unimodular (<em>PI</em>) formulation. At optimality, all three problems have the same objective value. A new way to tackle the LP problem is introduced: first solve the <em>Dc</em> and try to find Lagrange multipliers in order to build the <em>PI</em> model, from which an integer solution can be obtained directly. An implementation based on the discussed approaches was tested using IBM benchmarks.</p>