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# Dynamic Programming

• Date Submitted: 02/26/2013 09:16 AM
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Parvej Akhtar 11108212 A-15 Project Topic: Dynamic Programming and its Estimated Time: 2 months Nature of Project: Educational
Research

implementation

Project Introduction:-

Dynamic programming is an optimization approach that transforms a complex problem into a sequence of simpler problems; its essential characteristic is the multistage nature of the optimization procedure. More so than the optimization techniques described previously, dynamic programming provides a general framework for analyzing many problem types. Within this framework a variety of optimization techniques can be employed to solve particular aspects of a more general formulation. Usually creativity is required before we can recognize that a particular problem can be cast effectively as a dynamic program; and often subtle insights

are necessary to restructure the formulation so that it can be solved effectively.

Example:In order to introduce the dynamic-programming approach to solving multistage problems, in this section we analyze a simple example. Figure given below represents a street map connecting homes and downtown parking lots for a group of commuters in a model city. The arcs correspond to streets and the nodes correspond to intersections. The network has been designed in a diamond pattern so that every commuter must traverse five streets in driving from home to downtown.

Street map with intersection delays

The design characteristics and traffic pattern are such that the total time spent by any commuter between

intersections is independent of the route taken. However, substantial delays are experienced by the commuters in the intersections. The lengths of these delays in minutes are indicated by the numbers within the nodes. We would like to minimize the total delay any commuter can incur in the intersections while driving from his home to downtown.

How To Do It:The common way to do this is via lazy memoization. In some sense, the recursive Fibonacci function can be...