A Faster Algorithm for Computing Motorcycle Graphs

We present a new algorithm for computing motorcycle graphs that runs in O(n^4/3+ε) time for any ε >0 , 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 h holes in O(n √(h+1)log ^2 n+n^4/3+ε) expected time. If all input coordinates are O(log n) -bit rational numbers, we can compute the straight skeleton of a (possibly degenerate) polygon with h holes in O(n √(h+1)log ^3 n) expected time. In particular, it means that we can compute the straight skeleton of a simple polygon in O(nlog ^3n) expected time if all input coordinates are O(log n) -bit rationals, while all previously known algorithms have worst-case running time ω (n^3/2) .