We give an &Ogr;(n<supscrpt>3</supscrpt>·log n) time and &Ogr;(n<supscrpt>3</supscrpt>) space algorithm for the continuous homotopic one layer routing problem. The main contribution is an extension of the sweep paradigm to a universal cover space of the plane.
In this paper we introduce a general framework for com-paction on a torus. This problem comes up whenever an array of identical cells has to be compacted. We instantiate our framework with several specific compaction algorithms: one-dimensional compaction without and with automatic jog insertion and two-dimensional com-paction.