Here we present 1. a model for amplicon sequencing 2. a definition of the best assignment of a read to a set of reference sequences 3. strategies and structures for indexing reference sequences and computing the best assign- ments of a set of reads efficiently, based on (ultra)metric spaces and their geometry The models, techniques, and ideas are particularly relevant to scenarios akin to 16S taxonomic profiling, where both the number of reference sequences and the read diversity is considerable.