A linear time algorithm for wire sizing with simultaneous optimization of interconnect delay and crosstalk noise

TL;DR: A mathematical proof of existence for Nash equilibrium solution for the proposed wire sizing formulation is provided and the algorithm performs significantly better than simulated annealing and genetic search as established through experimental results.

Abstract: In this paper, we propose a new methodology for wire sizing with simultaneous optimization of interconnect delay and crosstalk noise in deep submicron VLSI circuits The wire sizing problem is modeled as an optimization problem formulated as a normal form game and solved using the Nash equilibrium Game theory allows the optimization of multiple metrics with conflicting objectives This property is exploited in modeling the wire sizing problem while simultaneously optimizing interconnect delay and crosstalk noise, which are conflicting in nature The nets connecting the driving cell and the driven cell are divided into net segments The net segments within a channel are modeled as players, the range of possible wire sizes forms the set of strategies and the payoff function is derived as the geometric mean of interconnect delay and crosstalk noise The net segments are optimized from the ones closest to the driven cell towards the ones at the driving cell The complete information about the coupling effects among the nets is extracted after the detailed routing phase The resulting algorithm for wire sizing is linear in terms of the number of wire segments in the given circuit Experimental results on several medium and large open core designs indicate that the proposed algorithm yields an average reduction of 2148% in interconnect delay and 2625% in crosstalk noise over and above the optimization from the Cadence place and route tools without any area overhead The algorithm performs significantly better than simulated annealing and genetic search as established through experimental results A mathematical proof of existence for Nash equilibrium solution for the proposed wire sizing formulation is provided