  In this paper we give a new, efficient algorithm for computing curve
skeletons, based on local separators. Our efficiency stems from a multilevel
approach, where we solve small problems across levels of detail and combine
these in order to quickly obtain a skeleton. We do this in a highly modular
fashion, ensuring complete flexibility in adapting the algorithm for specific
types of input or for otherwise targeting specific applications.
  Separator based skeletonization was first proposed by B{\ae}rentzen and
Rotenberg in [ACM Tran. Graphics'21], showing high quality output at the cost
of running times which become prohibitive for large inputs. Our new approach
retains the high quality output, and applicability to any spatially embedded
graph, while being orders of magnitude faster for all practical purposes.
  We test our skeletonization algorithm for efficiency and quality in practice,
comparing it to local separator skeletonization on the University of Groningen
Skeletonization Benchmark [Telea'16].
