Dynamic programming alignment of sequences representing cyclic patterns

String alignment by dynamic programming is generalized to include cyclic shift and corresponding optimal alignment cost for strings representing cyclic patterns. A guided search algorithm uses bounds on alignment costs to find all optimal cyclic shifts. The bounds are derived from submatrices of an initial dynamic programming matrix. Algorithmic complexity is analyzed for major stages in the search. The applicability of the method is illustrated with satellite DNA sequences and circularly permuted protein sequences