Optimization on operation sorting for HLS scheduling algorithms

High-Level Synthesis (HLS) automates hardware design from high-level language descriptions, enhancing design efficiency and reducing cycles. Operation scheduling, a critical step in HLS, determines system latency. Due to the NP-hard nature of scheduling problem, existing algorithms adopt heuristic approaches, scheduling operations sequentially. In this paper, we present a rigorous proof establishing the direct correspondence between the balanced state and the optimal scheduling. Additionally, we demonstrate the existence of operation scheduling sequences that achieve optimal results. Building on these findings, we propose a resource-constrained list scheduling algorithm. We introduce a novel priority function for the classic list scheduling algorithm to determine the scheduling order. Furthermore, we extend our approach to enhance the latency-constrained entropy-directed scheduling algorithm by altering the scheduling order. Experimental results validate the effectiveness of our novel priority function in addressing both resource-constrained and latency-constrained scheduling problems. Our algorithm achieves a near-optimal scheduling solution while maintaining low time complexity.