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**1 - 1**of**1**### Faster Reductions from Straight Skeletons to Motorcycle Graphs

, 2014

"... We give an algorithm that reduces the straight skeleton to the motorcycle graph in O(n log n) time for (weakly) simple polygons and O(n(log n) log m) time for a planar straight line graph with m connected com-ponents. The current fastest algorithms for computing motorcycle graphs are an O(n4/3+) tim ..."

Abstract
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We give an algorithm that reduces the straight skeleton to the motorcycle graph in O(n log n) time for (weakly) simple polygons and O(n(log n) log m) time for a planar straight line graph with m connected com-ponents. The current fastest algorithms for computing motorcycle graphs are an O(n4/3+) time algorithm for non-degenerate cases and O(n17/11+) for degenerate cases. Together with our algorithm this results in an algorithm computing the straight skeleton of a non-degenerate (weakly) simple polygon with r reflex vertices in O(n log n + r4/3+) time and of a non-degenerate planar straight line graph with m connected components in O(n(log n) logm+r4/3+) time. For degenerate cases the algorithm takes O(n log n+r17/11+) and O(n(log n) logm+ r17/11+) time respectively.