Interconnect Criticality-Driven Delay Relaxation

Abstract

Due to decreasing transistor sizes and increasing clock frequency, interconnect delay is a dominant factor in achieving timing closure in deep-submicrometer designs. In field programmable gate arrays (FPGA), interconnect delay is contributed by programmable routing switches. This increases the wire delay significantly. In FPGA devices, the interconnect delay is usually more than 40% of the total delay. Techniques like wire pipelining and retiming can manage delay of timing critical wires. However, the latency of the design limits the total pipelining in the design. Therefore, new techniques are needed at synthesis stage to consider the effect of critical wires in the design. In this paper, we propose an intuitive Critical Edge Reduction (CER) algorithm, which minimizes the number of critical wires on a maximal delay- budgeting solution under fixed latency constraint. We prove that this problem is NP-hard. We provide an integer linear programming formulation of the problem and an iterative heuristic algorithm (CER). During the course of our algorithm, we introduce multiple graph problems. We give a proof of NP-hardness of one such problem, which we call max arc-cost balancing problem. In our experiments, we present an in-depth analysis of tradeoff between various maximal budgetings and critical edge minimization. We implemented our design flow using a set of MediaBench datapaths on Xilinx VirtexE FPGA devices. Using our algorithm, the Xilinx Place-and-Route tool achieved timing closure, which is, on average, 2.8 times faster than using maximum budgeting. The resulting average clock period using CER algorithm outperforms the one using the maximum budgeting by 6%. Other results show similar advantages of critical edge minimization over traditional budgeting techniques.