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We give an algorithm for determining the distance between two vertices of thecomplex of curves. While there already exist such algorithms, for example byLeasure, Shackleton, and Webb, our approach is new, simple, and more effectivefor all distances accessible by computer. Our method gives a new preferredfinite set of geodesics between any two vertices of the complex, calledefficient geodesics, which are different from the tight geodesics introduced byMasur and Minsky.

Efficient geodesics and an effective algorithm for distance in the complex of curves