TAILIEUCHUNG - Lecture Algorithm design - Chapter 6: Dynamic programming I

Lecture Algorithm design - Chapter 6: Dynamic programming I include all of the following: Weighted interval scheduling, segmented least squares, knapsack problem, RNA secondary structure. | 6. Dynamic Programming I weighted interval scheduling segmented least squares knapsack problem RNA secondary structure Lecture slides by Kevin Wayne Copyright 2005 Pearson-Addison Wesley Copyright 2013 Kevin Wayne http wayne kleinberg-tardos Last updated on Jul 10 2015 6 26 AM Algorithmic paradigms Greedy. Build up a solution incrementally myopically optimizing some local criterion. Divide-and-conquer. Break up a problem into independent subproblems solve each subproblem and combine solution to subproblems to form solution to original problem. Dynamic programming. Break up a problem into a series of overlapping subproblems and build up solutions to larger and larger subproblems. fancy name for caching away intermediate results in a table for later reuse 2 Dynamic programming history Bellman. Pioneered the systematic study of dynamic programming in 1950s. Etymology. Dynamic programming planning over time. Secretary of Defense was hostile to mathematical research. Bellman sought an impressive name to avoid confrontation. THE THEORY OF DYNAMIC PROGRAMMING RICHARD BELLMAN 1. Introduction. Before turning to a discussion of some representative problems which will permit US to exhibit various mathematical features of the theory let US present a brief survey of the fundamental concepts hopes and aspirations of dynamic programming. To begin with the theory was created to treat the mathematical problems arising from the study of various multi-stage decision processes which may roughly be described in the following way We have a physical system whose state at any time t is determined by a set of quantities which we call state parameters or state variables. At certain times which may be prescribed in advance or which may be determined by the process itself we are called upon to make decisions which will affect the state of the system. These decisions are equivalent to transformations of the state variables the choice of a decision being identical with the

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