On the global fanout optimization problem

Fanout optimization is a fundamental problem in timing optimization. Most of the research has focussed on the fanout optimization problem for a single net (or the local fanout optimization problem-LFO). The real goal, however, is to optimize the delay through the entire circuit by fanout optimization, This is the global fanout optimization (GFO) problem. H. Touati (1990) claims that visiting nets of the network in a reverse topological order (from primary outputs to inputs), applying the optimum LFO algorithm to each net, computing the new required time at the source and propagating the delay changes to the fanins yields a provably optimum solution to the GFO problem. This result implies that GFO is solvable in polynomial time if LFO is. We show that that is not the case. We prove that GFO is NP-complete even if there are a constant number of buffering choices at each net. We analyze Touati's result and point out the flaw in his argument. We then present sufficient conditions for the optimality of the reverse topological algorithm.