The three phases of the Bowtie algorithm for the Maq-like policy. A three-phase approach finds alignments for two-mismatch cases 1 to 4 while minimizing backtracking. Phase 1 uses the mirror index and invokes the aligner to find alignments for cases 1 and 2. Phases 2 and 3 cooperate to find alignments for case 3: Phase 2 finds partial alignments with mismatches only in the hi-half, and phase 3 attempts to extend those partial alignments into full alignments. Finally, phase 3 invokes the aligner to find alignments for case 4.