A mapping apparatus comprises a mapper that translates from an input key to an output key in one or more storage devices. A pre-mapper for processing update operations comprises a plurality of mapping tablets and an in-memory look-up filter to identify a given mapping table storing a given input key. The mapping tablets comprise at least one dynamic in-memory ingress tablet and a plurality of persisted frozen tablets. For a given update operation, a first entry is added to one dynamic in-memory ingress tablet comprising the input key for the given update operation and a corresponding output key where data for the given update operation is stored; and a second entry is added to the look-up filter comprising the input key of the first entry and an identifier of the dynamic in-memory ingress tablet storing the first entry for the given update operation. The dynamic in-memory ingress tablet is persisted as a persisted frozen tablet. A given storage element is cloned by making a copy of the given storage element and assigning a new internal identifier to the given storage element and the copy.