IMPROVING SIZE-BOUNDS FOR SUBCASES OF SQUARE-SHAPED SWITCHBOX ROUTING1

Various problems are studied in the field of detailed VLSI routing. According to the position of the terminals on the outer boundaries of a rectangular grid, one can distinguish between different subcases of Switchbox Routing: C-shaped, Gamma, Channel and Single Row Routing. This paper focuses on the minimum number of layers needed for solving these problems either in the Manhattan, or in the unconstrained wiring model. Besides summarizing earlier known bounds, our new results show examples for C-shaped routing problem instances of arbitrary size that cannot be solved using 3 layers in the Manhattan, or 2 layers in the unconstrained model.