Optimal multi-domain clock skew scheduling

Abstract

Clock skew scheduling is an effective technique to improve the performance of sequential circuits. However, with process variations, it becomes more difficult to implement a large number of clock delays in a precise manner. Multi-domain clock skew scheduling is one way to overcome this limitation. In this paper, we prove the NP-completeness of multi-domain clock scheduling problem, and design a practical optimal algorithm to solve it. Given the domain number, we bound the number of all possible skew assignments and develop an optimal algorithm with efficient pruning techniques. Experiment results on ISCAS89 sequential benchmarks show the optimality and efficiency of our method compared with existing approaches.

Multi-parameter clock skew scheduling

“…They demonstrate that by restricting the clock latency into a few domains, the clock tree can be implemented more practically while the performance does not degrade too much. However, the MDCSS problem is a discrete problem and is proved to be NP-hard [14]. Several heuristic methods have been proposed to solve this problem [15][16][17][18].…”

2-SAT based linear time optimum two-domain clock skew scheduling

“…An exact algorithm based on branch-and-bound search framework with greedy speeding up heuristics was proposed in [8]. In [9], it is proved that MDCSS problem is NP-complete when the number of clock domains is |V|/2, where |V| is the number of registers. Moreover, in [9], the algorithm was proposed to obtain an optimum clock skew schedule.…”

“…In [9], it is proved that MDCSS problem is NP-complete when the number of clock domains is |V|/2, where |V| is the number of registers. Moreover, in [9], the algorithm was proposed to obtain an optimum clock skew schedule. The time complexity of the algorithm proposed in [9] is O((k − 1)!|V||E| k ), where k is the number of clock domains, |V| is the number of registers, and |E| is the number of register pairs with signal propagations.…”

“…Moreover, in [9], the algorithm was proposed to obtain an optimum clock skew schedule. The time complexity of the algorithm proposed in [9] is O((k − 1)!|V||E| k ), where k is the number of clock domains, |V| is the number of registers, and |E| is the number of register pairs with signal propagations. It means that MD-CSS problem can be solved in polynomial time if the number of clock domains is restricted to a small constant.…”

“…Therefore, the fast two-domain clock skew scheduling algorithm is desired in practical circuit design to improve the circuit performance by a practical clock distribution network. However, the algorithm in [9] takes to much time since the time complexity of the algorithm in [9] is O(|V||E| 2 ) when k = 2.…”