Wirability of knock-knee layouts with 45° wires

The problem of wiring an arbitrary knock-knee layout (in a square grid with an arbitrary number of modules) in three and two layers using a small number of vias is investigated. A technique is proposed for transforming a knock-knee layout into a three-layer wirable layout by replacing knock-knees with 45° wires. A 45° replacing algorithm to achieve three-layer wirability is introduced. An efficient stretching technique to ensure two-layer wirability using 45° wires is described. Conversion of an abstract layout into a corresponding physical layout is discussed. Experimental results are presented