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We present a method for microtubule tracking in electron microscopy volumes. Our method first identifies a sparse set of voxels that likely belong to microtubules. Similar to prior work, we then enumerate potential edges between these voxels, which we represent in a candidate graph. Tracks of microtubules are found by selecting nodes and edges in the candidate graph by solving a constrained optimization problem incorporating biological priors on microtubule structure. For this, we present a novel integer linear programming formulation, which results in speed-ups of three orders of magnitude and an increase of 53% in accuracy compared to prior art (evaluated on three 1.2 x 4 x 4$μ$m volumes of Drosophila neural tissue). We also propose a scheme to solve the optimization problem in a block-wise fashion, which allows distributed tracking and is necessary to process very large electron microscopy volumes. Finally, we release a benchmark dataset for microtubule tracking, here used for training, testing and validation, consisting of eight 30 x 1000 x 1000 voxel blocks (1.2 x 4 x 4$μ$m) of densely annotated microtubules in the CREMI data set (https://github.com/nilsec/micron).