Non-tree routing

An implicit premise of existing routing methods is that the routing topology must correspond to a tree (i.e. it does not contain cycles). In this paper we investigate the consequences of abandoning this basic axiom, and instead allow routing topologies that correspond to arbitrary graphs (i.e. where cycles are admissible). We show that adding extra wires to an existing routing tree can often significantly improve signal propagation delay by exploiting a tradeoff between wire capacitance and resistance, and we propose a new routing algorithm based on this phenomenon. Using SPICE to determine the efficacy of our methods, we obtain dramatic results: for example, the judicious addition of a few extra wires to an existing Steiner routing reduces the signal propagation delay by an average of up to 62%, with relatively modest total wirelength increase, depending on net size and the technology parameters. Finally, we observe that non-tree routing also significantly reduces signal skew