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Scalable real-time assortment optimization has become essential in e-commerce operations due to the need for personalization and the availability of a large variety of items. While this can be done when there are simplistic assortment choices to be made, the optimization process becomes difficult when imposing constraints on the collection of relevant assortments based on insights by store-managers and historically well-performing assortments. We design fast and flexible algorithms based onarXiv:2003.04736v2 fatcat:uvkg7noai5g4bcjell7i2jsp3a