Chapter 12. Dynamic Programming

Dynamic programming (DP) is a commonly used technique for solving a wide variety of discrete optimization problems such as scheduling, string-editing, packaging, and inventory management. More recently, it has found applications in bioinformatics in matching sequences of amino-acids and nucleotides (the Smith-Waterman algorithm). DP views a problem as a set of interdependent subproblems. It solves subproblems and uses the results to solve larger subproblems until the entire problem is solved. In contrast to divide-and-conquer, where the solution to a problem depends only on the solution to its subproblems, in DP there may be interrelationships across subproblems. In DP, the solution to a subproblem is expressed as a function of solutions to one or more subproblems at the preceding levels.