Easy and difficult exact covering problems arising in VLSI power reduction by clock gating

Several graph matching and exact covering problems arising in VLSI low-power design optimization by clock gating are presented. To maximize the power savings, clock gating requires optimal grouping of Flip-Flops (FFs), which depends on FFs' data toggling correlations and probabilities. These naturally lead to optimal matching and exact covering problems. We present three problems arising by different clock-gating techniques. In a method called data-driven clock-gating, the corresponding covering problem is intractable but can practically be solved by appropriate heuristics. In another method called multi-bit flip-flops, the covering problem is easily solvable in a closed-form, required only sorting. We finally present the covering problem arising in a new method called look-ahead clock-gating, for which the question of whether the exact covering problem is easy or difficult is left open.