“…The second summation reflects the lengths of the wires entering a multiplexer standard cell, expressed in multiples of the height of the subtree, assuming the destination standard cell is placed at the median height. For the worst-case tree, the total length of wires in a multiplexer tree is given by (14) Therefore, the total length of wires in the average-case tree is (15) Assuming all wires are long distance wires with a 6 width and 10 pitch, a worst-case assumption, then the following vertical wire routing constraint must also be recognized: the total area used to route vertical wires must be realizable on layers of metal given the area of the switch, i.e., (16) Our analysis indicates that this vertical wiring routing constraint is met for the 0.18-m CMOS process with six or more layers of metal, for switches of degree 2. However for degree 4 or 8 multiplexers, the area consumed by routing vertical wires increases, and this constraint may not be met, in which case the area of the switch must be increased until (16) holds.…”