A Faster Algorithm for Computing Motorcycle Graphs

Abstract

We present a new algorithm for computing motorcycle graphs that runs in time for any , improving on all previously known algorithms. The main application of this result is to computing the straight skeleton of a polygon. It allows us to compute the straight skeleton of a non-degenerate polygon with holes in expected time. If all input coordinates are -bit rational numbers, we can compute the straight skeleton of a (possibly degenerate) polygon with holes in expected time. In particular, it means that we can compute the straight skeleton of a simple polygon in expected time if all input coordinates are -bit rationals, while all previously known algorithms have worst-case running time