Efficient Method for Computing Critical Path Delay using Longest Path Matrix Algorithm

Iterative algorithms are a fundamental component of numerous computational tasks, from numerical simulations to optimization problems. To ensure the efficiency and reliability of these iterative processes, it is crucial to determine suitable iteration bounds that balance computational cost and accuracy. Recent techniques to compute critical path delay like Machine Learning-based approaches. Path Sensitization techniques heavily rely on historical data. Hence changes in the initial conditions and inaccuracies in data often lead to unreliable predictions and result in significant deviation. Canonicity is important in multipliers to reduce complexity and DSP filters like IIR and FIR filters, whose stability decides the performance of the system. In this research work, a novel approach utilizing the Longest Path Matrix Algorithm(LPM) is presented, commonly known as the Critical Path Method (CPM). It is the ability to identify the longest path in a Directed Acyclic Graph (DAG) involving delays between nodes for complex networks. Multi-rate DAGs can be used but it contains many redundant nodes and edges. It provides a deterministic approach and involves matrix-based operations to compute critical paths, thus achieving precise, efficient and predictable results. CPM involves constructing, manipulating matrices and computing iteration bounds, which can be efficiently handled in MATLAB. Thus, it offers a robust and versatile solution for a wide range of iterative problems thereby optimizing the convergence of iterative algorithms. Minimum cycle mean algorithm is a better method than LPM with a lower polynomial time complexity. The DAG is implemented in Xilinx Vivado software to obtain the resource and power utilization for the various matrices obtained. The DAG used for LPM is applied to various filters like pipelined FIR filter, clustered lookahead pipelined filter and all pole lattice filter and their resource utilization is tabulated.