Speeding Up Dynamic Programming without Omitting any Optimal Solution and Some Applications in Molecular Biology

We extend the algorithm of Galil and Giancarlo, which speeds up dynamic programming in the case of concave cost functions, such that a compact representation of all optimal solutions is computed. Compared to the Galil–Giancarlo algorithm our time bound grows only by a small constant factor. With a compact representation, we develop efficient algorithms for the solution of problems in molecular biology concerning the computation of all optimal local alignments and all optimal subalignments in genetic sequences.