Fidelity and near-optimality of Elmore-based routing constructions

We address the efficient construction of interconnection trees with near-optimal delays. We study the accuracy and fidelity of easily-computed delay models with respect to detailed simulation (e.g., SPICE-computed delays). We show that Elmore delay minimization (W.C. Elmore, 1948) is a high-fidelity interconnect objective for IC interconnect technologies, and propose a greedy low delay tree (LDT) heuristic which for any monotone delay function can efficiently minimize maximum delay. For comparison, we also generate optimal routing trees (ORTs) with respect to Elmore delay, using branch-and-bound search. Experimental results show that the LDT heuristic approximates ORTs very accurately: for nets with up to seven pins, LDT trees have a maximum sink delay within 2.3% of optimum on average. Moreover, compared with minimum spanning tree constructions, the LDT achieves average reductions in delay of up to 35% depending on the net size