Inverse theorem in dynamic programming II

Optimization II: Dynamic Programming

In the last chapter, we saw that greedy algorithms are efficient solutions to certain optimization problems. However, there are optimization problems for which no greedy algorithm exists. In this chapter, we will examine a more general technique, known as dynamic programming, for solving optimization problems. Dynamic programming is a technique of implementing a top-down solution using bottom-u...

Lecture 25 — Dynamic Programming II

The top-down approach is based on running the recursive code as is, generating implicitly the recursion structure from the root of the DAG down to the leaves. Each time a solution to a smaller instance is found for the first time it generates a mapping from the input argument to its solution. This way when we come across the same argument a second time we can just look up the solution. This pro...

Approximate Dynamic Programming—ii: Algorithms

• Option Pricing. An American option allows us to buy or sell an asset at any time up to a specified time, where we make money when the price goes under or over (respectively) a set strike price. Valuing the option requires finding an optimal policy for determining when to exercise the option. • Playing Games. Computer algorithms have been designed to play backgammon, bridge, chess, and recentl...

Declarative Dynamic Programming as an Alternative Realization of Courcelle's Theorem

Many computationally hard problems become tractable if the graph structure underlying the problem instance exhibits small treewidth. A recent approach to put this idea into practice is based on a declarative interface to specify dynamic programming over tree decompositions, delegating the computation to dedicated solvers. In this paper, we prove that this method can be applied to any problem wh...

Theorem Proving and Programming with Dynamic First Order Logic