Bounding the load capacitance at gate outputs is a standard element in today's electrical correctness methodologies for high-speed digital very large scale integration design. Bounds on load caps improve coupling-noise immunity, reduce degradation of signal transition edges, and reduce delay uncertainty due to coupling noise (Kahng et al. 1998). For clock and test distribution, an additional design requirement is bounding the buffer skew, i.e., the difference between the maximum and the minimum number of buffers over all of the source-to-sink paths in the routing tree, since buffer skew is one of the main factors affecting delay skew (Tellez and Sarrafzadeh 1997). In this paper, we consider algorithms for buffering a given tree with the minimum number of buffers under given load cap and buffer skew constraints. We show that the greedy algorithm proposed by Tellez and Sarrafzadeh is suboptimal for nonzero buffer-skew bounds and give examples showing that no bottom-up greedy algorithm can achieve optimality. The main contribution of the paper is an optimal dynamic programming algorithm for the problem. Experiments on test cases extracted from recent industrial designs show that the dynamic programming algorithm has practical running time and saves up to 37.5% of the buffers inserted by Tellez and Sarrafzadeh's algorithm.

In high-speed digital VLSI design, bounding the load capacitance at gate outputs is a well-known methodology to improve coupling noise immunity, reduce degradation of signal transition edges, and reduce delay uncertainty due to coupling noise. Bounding load capacitance also improves reliability with respect to hot-carrier oxide breakdown and AC self-heating in interconnects, and guarantees bounded input rise/fall times at buffers and sinks. This paper introduces a new minimum-buffer routing problem (MBRP) formulation which requires that the capacitive load of each buffer, and of the source driver, be upper-bounded by a given constant. Our contributions are as follows: .We give linear-time algorithms for optimal buffering of a given routing tree with a single (inverting or noninverting) buffer type. .For simultaneous routing and buffering with a single noninverting buffer type, we prove that no algorithm can guarantee a factor smaller than 2 unless P = NP and give an algorithm with approximation factor slightly larger than 2 for typical buffers. For the case of a single inverting buffer. type, we give an algorithm with approximation factor slightly larger than 4. .We give local-improvement and clustering based MBRP heuristics with improved practical performance, and present a comprehensive experimental study comparing the runtime/quality tradeoffs of the proposed MBRP heuristics on test cases extracted from recent industrial designs.

Background and purpose

Materials and methods

Results

Conclusions