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We present a new approach to VLSI placement legalization. Based on a minimum-cost flow algorithm that iteratively augments flows along paths, our algorithm ensures that only augmentations are considered that can be realized exactly by cell movements. Hence, the method avoids realization problems which are inherent to previous flow-based legalization algorithms. As a result, it combines the global perspective of minimum-cost flow approaches with the efficiency of local search algorithms. The tool is mainly designed to minimize total and maximum cell movement but it is flexible enough to optimize the effect on timing or netlength, too. We compare our approach to legalization tools from industry and academia by experiments on dense recent real-world designs and public benchmarks. The results show that we are much faster and produce significantly better results in terms of average (linear and quadratic) and maximum movement than any other tool.