The meaning of biological sequences is a central problem of modern biology. Although string matching is well understood in the edit-distance model, biological strings with transpositions and inversions violate this model's assumptions. To align biologically reasonable strings, we proposed the Walking Tree Method, an approximate string alignment method that can handle insertion, deletions, substitutions, translocations, and more than one level of inversions. Our earlier versions were able to align whole bacterial genomes (approx.1 Mbps) and discover and verify genes. As extremely long sequences can now be deciphered rapidly and accurately without amplification, speeding up the method becomes necessary. Via a technique that we call it "recurrence reduction" in which same computations can be looked up rather than recomputed, we are able to significantly improve the performance, e.g., 400% for 1-million base pair alignments.