Integer Linear Programming Models for Global Routing
INFORMS Journal on Computing
On routing in VLSI design and communication networks
Discrete Applied Mathematics
A multilevel congestion-based global router
VLSI Design
On routing in VLSI design and communication networks
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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This paper investigates the global routing problem for integrated circuits. We introduce a formulation on the basis of integer programming which minimizes the routing area among a limited set of Steiner trees for each net. Indeed, the involved cost function depends on the channel density of the routing which has a direct influence on the routing area.Our methods for solving the global routing problem employ local search heuristics, sequential routing, genetic routing, and randomized procedures. Our methods for computing lower bounds are based on linear and Lagrange relaxation. An analysis on the tightness of the bounds indicates that the difference between the cost of the optimal integer solutions and the cost of the optimal fractional solutions is only a small number of tracks in practice. Moreover, the analysis leads to the concept of linear preprocessing by which we exclude a large number of high-cost solutions.We introduce several versions of preprocessing, one of which preserves the opportunity of obtaining a globally optimal solution in general; all of them do so in practice. Linear preprocessing enables us to solve problem instances with several thousand nets provably optimal or at least provably close to optimal.All methods have been implemented in the software package Eridanus. We present computational results.The global routing problem assumes the placement of the chip components to be fixed. An extension of the problem, which we call global layout of integrated circuits, allows the placement to be variable and searches for a placement that minimizes the routing area among a limited set of alternatives. We show that the results concerning the global routing problem can be easily extended to global layout.