c ○ Alexander Karl Hudek 2010I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Pairwise sequence alignment is a fundamental problem in bioinformatics with wide applicability. This thesis presents three new algorithms for this well-studied problem. First, we present a new algorithm, RDA, which aligns sequences in small segments, rather than by individual bases. Then, we present two algorithms for aligning long genomic sequences: CAPE, a pairwise global aligner, and FEAST, a pairwise local aligner. RDA produces interesting alignments that can be substantially different in structure than traditional alignments. It is also better than traditional alignment at the task of homology detection. However, its main negative is a very slow run time. Further, although it produces alignments with different structure, it is not clear if the differences have a practical value in genomic research. Our main success comes from our local aligner, FEAST. We describe two main improvements: