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We introduce and develop models for very high density physical goods storage systems, which are characterized by sometimes having to move interfering items in order to gain access to desired items. We describe a simple but effective algorithm to densely fill rectangular storage spaces, subject to a constraint on the number of interfering items. We also prove an upper bound on storage density for any rectangular space, including traditional warehouses.doi:10.1080/07408170500247352 fatcat:oom5ef4lafck3b4wko2djpdoqi