Recursion schemes for dynamic programming

Authors:
Jevgeni Kabanov;Varmo Vene
Affiliations:
Dept. of Computer Science, University of Tartu, Tartu, Estonia;Dept. of Computer Science, University of Tartu, Tartu, Estonia
Venue:
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Year:
2006

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Abstract

Dynamic programming is an algorithm design technique, which allows to improve efficiency by avoiding re-computation of identical subtasks. We present a new recursion combinator, dynamorphism, which captures the dynamic programming recursion pattern with memoization and identify some simple conditions when functions defined by structured general recursion can be redefined as a dynamorphism. The applicability of the new recursion combinator is demonstrated on classical dynamic programming algorithms: Fibonacci numbers, binary partitions, edit distance and longest common subsequence.