Generalized Voronoi diagrams for a ladder: II. Efficient construction of the diagram

We present a collection of algorithms, all running in timeO(n² logn (n)^o((n)3)) for some fixed integers(where (n) is the inverse Ackermann's function), for constructing a skeleton representation of a suitably generalized Voronoi diagram for a ladder moving in a two-dimensional space bounded by polygonal barriers consisting ofn line segments. This diagram, which is a two-dimensional subcomplex of the dimensional configuration space of the ladder, is introduced and analyzed in a companion paper by the present authors. The construction of the diagram described in this paper yields a motion-planning algorithm for the ladder which runs within the same time bound given above.Work on this paper has been supported in part by Office of Naval Research Grant N00014-82-K-0381, and by grants from the Digital Equipment Corporation, the Sloan Foundation, the System Development Foundation, the IBM corporation, and by National Science Foundation CER Grant No. DCR-8320085. Work by the second author has also been supported in part by a grant from the US-Israeli Binational Science Foundation.