Recent advances in long-read sequencing technology enable its use in potentially life-saving applications for rapid clinical diagnostics and epidemiological monitoring. To take advantage of these enabling characteristics, we present Voyager, a novel algorithm that complements real-time sequencing by rapidly and efficiently mapping long sequencing reads with insertion- and deletion errors to a large set of reference genomes. The concept of Sorted Motif Distance Space (SMDS), i.e., distances between exact matches of short motifs sorted by rank, represents sequences and sequence complementarity in a highly compressed form and is thus computationally efficient while enabling strain-level discrimination. In addition, Voyager applies a deconvolution algorithm rather than reducing taxonomic resolution if sequences of closely related organisms cannot be discerned by SMDS alone. Using relevant real-world data, we evaluated Voyager against the current best taxonomic classification methods (Kraken 2 and Centrifuge). Voyager was on average more than twice as fast as the current fastest method and obtained on average over 40% higher species level accuracy while maintaining lower memory usage than both other methods.