Multiterminal-net routing by grid stretching

Let R be a rectangle uniformly partitioned by w-1 vertical line segments and h-1 horizontal line segments. The problem of routing through the rectangle, called the RRP problem (also referred to as the switch-box routing problem), is considered. It is denoted by I=(R, N), and consists of finding a layout under the knock-knee wiring model for the set N of nets inside R. The authors present a set of transformations different from the ones given by K. Mehlhorn et al. (Journal of ACM, vol.33, no.1, p.60-85, 1986) that provide smaller approximation bounds for the unrestricted RRP and the three-terminal-net RRP problems