Flexible optimal channel routing for critical nets

Abstract

A theoretical basis is presented from which two main results follow, a tight lower bound for the total wiring length of a multi terminal net channel routing, and a set of rules that determine how much routings can be obtained. Algorithmic implementations of the rules have computational complexity O( n). The theory also shows that a net can have multiple minimum wiring length routings, and how all of them can be found. An obvious application of the theory is in the critical net channel routing, where main objectives are minimizations of the wiring length and the number of vias. Those objectives are usually met by prerouting the critical nets before other signal nets, which then find the critical net wiring as an obstacle in the channel. The multiplicity of optimal critical net routings translates into the flexibility of obstacles. Partitioning of a multi terminal net into the flexible and rigid subnets provides a kind of computer vision for the obstacle flexibility.