Simplifying Dynamic Programming via Tabling

Abstract

In the dynamic programming paradigm the value of an optimal solution is recursively defined in terms of optimal solutions to subproblems. Such dynamic programming definitions can be very tricky and error-prone to specify. This paper presents a novel, elegant method based on tabled logic programming that simplifies the specification of such dynamic programming solutions. Our method introduces a new mode declaration for tabled predicates. The arguments of each tabled predicate are divided into indexed and non-indexed ones so that tabled predicates can be regarded as functions: indexed arguments represent input values and non-indexed arguments represent output values. The non-indexed arguments in a tabled predicate can be further declared to be aggregate, e.g., the minimum, so that while generating answers, the global table will dynamically maintain the smallest value for that argument. This mode declaration scheme, coupled with recursion, provides a considerably easy-to-use method for dynamic programming: there is no need to define the value of an optimal solution recursively, instead, defining a general solution suffices. The optimal value as well as its corresponding concrete solution can be derived implicitly and automatically using tabled logic programming systems. Experimental results are shown to indicate that the mode declaration improves both time and space performances in solving dynamic programming problems on tabled LP systems. Additionally, our mode declaration scheme provides an alternative implementation vehicle for preference logic programming.

This research is supported by NSF Nebraska EPSCoR grant.