Sparse dynamic programming I: linear cost functions

David Eppstein, Zvi Galil, Raffaele Giancarlo, Giuseppe F. Italiano
1992 Journal of the ACM  
Dynamic programming solutlons to a number of different recurrence equations for sequence comparison and for RNA secondary structure prediction are considered. These recurrences are defined over a number of points that is quadratic in the input size; however only a sparse set matters for the result. Efficient algorithms for these problems are given, when the weight functions used in the recurrences are taken to be linear. The time complexity of the algorithms depends almost linearly on the
more » ... nearly on the number of points that need to be considered; when the problems are sparse this results in a substantial speed-up over known algorithms.
doi:10.1145/146637.146650 fatcat:3nzl4wdeszcf7kzolb2pu43irm