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Topic: Dynamic programming

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	Dynamic Programming
		Less widely known applications of dynamic programming are in parsing and in programs to play chess; both gain significant benefits from a Dynamic Programming formulation.
		Dynamic programming is the basis of comparison and alignment routines - such as the unix diff routine.
		Using dynamic programming it is possible for an algorithm to evaluate all possible ways of aligning one sequence against another in a reasonable time, even though the number of such possible alignments grows exponentially with the length of the two sequences.
	www.catalase.com /dprog.htm (1191 words)

	Cprogramming.com - Tutorials - Dynamic Programming
		Dynamic programming is a powerful technique for solving problems that might otherwise appear to be extremely difficult to solve in polynomial time.
		Often, dynamic programming algorithms are visualized as "filling an array" where each element of the array is the result of a subproblem that can later be reused rather than recalculated.
		Dynamic programming produces a simpler, cleaner algorithm (though one that is not inherently faster).
	cprogramming.com /tutorial/computersciencetheory/dp.html (962 words)

	Dynamic programming - Wikipedia, the free encyclopedia
		Some programming languages with special extensions [1] can automatically memoize the result of a function call with a particular set of arguments, in order to speed up call-by-name evaluation (this mechanism is referred to as call-by-need).
		In interactive image processing programs, dynamic programing may be used within the algorithm supporting a "magnetic" edge following selection tool, where the paths that exhibit small change in color or brightness along the path have a lower cost compared to alternate paths that cross edges.
		An accessible introduction to dynamic programing in economics.
	en.wikipedia.org /wiki/Dynamic_programming (1629 words)

	Models - Operations Research Models and Methods
		Because the word dynamic describes situations that occur over time and programming is a synonym for planning, the original definition of dynamic programming was "planning over time." In a limited sense, our concern is with decisions that relate to and affect phenomena that are functions of time.
		To model with dynamic programming, an abstraction or reduction of complexity from the real world problem is necessary.
		Dynamic programming has been described as the most general of the optimization approaches because conceivably it can solve the broadest class of problems.
	www.me.utexas.edu /~jensen/ORMM/models/unit/dynamic/index.html (460 words)

	Dynamic Programming (Site not responding. Last check: 2007-09-15)
		Dynamic Programming is an approach developed to solve sequential, or multi-stage, decision problems; hence, the name "dynamic" programming.
		Dynamic programming, like branch and bound approach, is a way of decomposing certain hard to solve problems into equivalent formats that are more amenable to solution.
		In terms of dynamic programming formulation, the "state" of this inventory process is completely described by the level of beginning inventory at each period.
	www.ie.bilkent.edu.tr /~omer/research/dynprog.html (2366 words)

	CSE 392 - Programming Challenges Dynamic Programming (Week 11) (Site not responding. Last check: 2007-09-15)
		Dynamic programming is a very powerful, general tool for solving optimization problems on left-right-ordered items such as character strings.
		Dynamic programming algorithms are defined by recursive algorithms/functions that describe the solution to the entire problem in terms of solutions to smaller problems.
		Dynamic programming is a technique for efficiently implementing a recursive algorithm by storing partial results.
	www.cs.sunysb.edu /~skiena/392/lectures/week11 (1574 words)

	Dynamic programming language - Wikipedia, the free encyclopedia
		Dynamic programming language is a term used broadly in computer science to describe a class of high level programming languages which share many common runtime behaviors that other languages only perform during compilation, if at all.
		Dynamic languages and dynamic typing are not identical concepts, and a dynamic language need not be dynamically typed, though many dynamic languages are dynamically typed.
		One of the most widely used aspects of functional programming in dynamic languages is the closure, which allows creating a new instance of a function which retains access to the context in which it was created.
	en.wikipedia.org /wiki/Dynamic_programming_language (860 words)

	Lecture notes: 3. Algorithm for sequence alignment: dynamic programming (Site not responding. Last check: 2007-09-15)
		The word "programming" does not mean that it has to be a computer program; this is just mathematical jargon for using a fixed set of rules to arrive at a solution.
		Dynamic programming, a simple variant, with no gap penalties and a simple substitution scoring scheme.
		Dynamic programming, a more advanced variant, with gap penalties and a slightly more complicated substitution scoring scheme.
	www.sbc.su.se /~per/molbioinfo2001/seqali-dyn.html (548 words)

	ALATE Dynamic Programming Overview
		We exploit the fact that the dynamic programming is essentially determining minimal weight paths of length n in a finite state space, and must ultimately reach a periodic solution (which can be detected).
		The high dimensionality encountered means that the array rapidly decreases as the dynamic programming proceeds, which forces processors to continually shift the index ranges that they are working on.
		He is also working on programs for several other aspects of adaptive designs, and more generally on the problem of producing efficient highly parallel programs for dynamic programming.
	www.eecs.umich.edu /~qstout/dynamprog.html (2081 words)

	Dynamic Programming - Algorithmist
		Dynamic Programming is a technique that takes advantage of overlapping subproblems, optimal substructure, and trades space for time to improve the runtime complexity of algorithms.
		In Bottom Up Dynamic Programming, we start from smaller cases and store the calculated values in a table for future use, an effective strategy to most dependency-based problems.
		Dynamic Programming (DP) generates all enumerations, or rather, cases of the smaller breakdown problems, leading towards the larger cases, and eventually it will lead towards the final enumeration of size n.
	www.algorithmist.com /index.php/Dynamic_Programming (500 words)

	Fabulous Adventures In Coding : Recursion and Dynamic Programming (Site not responding. Last check: 2007-09-15)
		Dynamic programming isn't hard, but a lot of script programmers don't know about this powerful technique, so I thought I might talk about it a bit today.
		And dynamic programming was already being applied to general computer and engineering problems the same year that Bellman's original dynamic programming book was published.
		Technically, dynamic programming is an algorithmic technique that applies only to a certain class of optimization problems, and it's iterative by its very nature, so you have to be "really being clever".
	blogs.msdn.com /ericlippert/archive/2004/07/21/189974.aspx (1973 words)

	WORMS Virtual Encyclopedia
		Beckmann, M., Dynamic Programming of Economic Decisions, Springer-Verlag, New York, 1968.
		Nemhauser, G.L., Introduction to Dynamic Programming, Wiley, New York, 1966.
		Dynamic programming (DP) is an approach to problem solving based on
	www.worms.ms.unimelb.edu.au /encyclopedia/topics/dp.html (2296 words)

	Lecture 12 - introduction to dynamic programming
		Dynamic Programming is a technique for computing recurrence relations efficiently by sorting partial results.
		Dynamic programming is a technique for efficiently computing recurrences by storing partial results.
		Dynamic programming is best understood by looking at a bunch of different examples.
	www.cs.sunysb.edu /~algorith/lectures-good/node12.html (1163 words)

	String Alignment using Dynamic Programming
		Dynamic programming is an algorithm in which an optimization problem is solved by saving the optimal scores for the solution of every subproblem instead of recalculating them.
		A matrix D is created to save the optimal dynamic programming scores for every pair of substrings up to that point.
		The first row and column of the dynamic programming matrix are the scores of aligning the subsequences s[1..j] and t[1..i] against a string of gaps of length j or i, respectively.
	www.biorecipes.com /DynProgBasic/code.html (1675 words)

	Dynamic programming: an introduction (Site not responding. Last check: 2007-09-15)
		Dynamic programming was the brainchild of an American Mathematician, Richard Bellman, who described the way of solving problems where you need to find the best decisions one after another.
		The dynamic programming approach to the potential partner problem starts by thinking about what happens when faced with the last partner.
		One of the characteristics of dynamic programming is that the solution to smaller problems is built into that of larger ones.
	plus.maths.org /issue3/dynamic (903 words)

	ENGnetBASE: Engineering Handbooks Online
		Dynamic programming is a powerful method for solving optimization problems, but has a number of drawbacks that limit its use to solving problems of very low dimension.
		With iteration, dynamic programming becomes an effective optimization procedure for very high-dimensional optimal control problems and has demonstrated applicability to singular control problems.
		Recently, iterative dynamic programming (IDP) has been refined to handle inequality state constraints and noncontinuous functions.
	www.engnetbase.com /ejournals/books/book_summary/summary.asp?id=864 (159 words)

	Joel Pobar's CLR weblog : CLR Dynamic languages under the hood (Part 1 of many) (Site not responding. Last check: 2007-09-15)
		Of course, dynamic languages are a whole lot more than this, I’ve just constrained this post to ideas around those particular aspects.
		REPL’s are usually quite simple command line programs that read in a line of text and feed that to a compiler or interpreter for statement or expression evaluation.
		Religious wars on whether dynamic languages are a good thing or not aside (and I'm sure there'll always be people for or against), a pretty cool write up.
	blogs.msdn.com /joelpob/archive/2005/07/01/434728.aspx (3588 words)

	Dynamic Websites : Programming & Forms
		Dynamic websites means that different actions by the visitor cause different behaviors, i.e.
		backend or server side programming is far more reliable than front end or client side programming.
		And each browser, each version of each browser, and in fact each version of each browser on each OS such as Windows, Mac OS, or Linux is a different program often with a different version of Javascript on it.
	face2interface.com /MYD/Developer_Tips/Programming.shtml (248 words)

	Brian's Digest: Dynamic programming
		There are a number of optimization programs being developed at universities that have widely varying levels of sophistication regarding log shape and breakdown optimization considerations.
		Dynamic programming essentially is a technique whereby you break the problem down into a series of smaller -- chained problems.
		Dynamic programming is essentially bottom-up recursion where you store the answers in a table starting from the base case(s) and building up to larger and larger parameters using the recursive rule(s).
	www.worms.ms.unimelb.edu.au /digest/dp97.html (2138 words)

	Dynamic Programming Algorithm, Edit Distance
		If a computer program on machine-1 is being used by someone from a screen on (distant) machine-2, e.g.
		One approach is for the program (on machine-1) to keep a "picture" of what the screen currently is (on machine-2) and another picture of what it should become.
		If your programming language does not support 2-dimensional arrays, and requires arrays or strings to indexed from zero upwards, some home-grown address translation will be needed to program the DPA defined above.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Dynamic/Edit (1208 words)

	Dynamic programming
		Dynamic programming can be thought of as being the reverse of recursion.
		Dynamic programming is a bottom-up mechanism -- we solve all possible small problems and then combine them to obtain solutions for bigger problems.
		The reason that this may be better is that, using recursion, it is possible that we may solve the same small subproblem many times.
	www.ics.uci.edu /~dan/class/161/notes/6/Dynamic.html (699 words)

	[No title] (Site not responding. Last check: 2007-09-15)
		Dynamic Programming is an important problem-solving technique that has been widely used in various fields such as operations research, computer science, control theory and biology.
		The Dynamic Programming technique works by associating to the optimization problem an automaton with costs:
		The implementation of the Dynamic Programming skeleton is contained in four files:
	nereida.deioc.ull.es /~cicyt/mallbaDP (776 words)

	Neuro-Dynamic Programming
		In practice, however, the applicability of dynamic programming to many important problems is limited by the enormous size of the underlying state spaces (Bellman's "curse of dimensionality").
		Neuro-dynamic programming (or "Reinforcement Learning", which is the term used in the Artificial Intelligence literature) uses neural network and other approximation architectures to overcome such bottlenecks to the applicability of dynamic programming.
		Starting with a good heuristic and carrying out what is essentially a single policy iteration (in the dynamic programming sense) provides a systematic method for improving the performance of a heuristic, and has great promise in practical settings.
	web.mit.edu /jnt/www/ndp.html (1160 words)

	Lecture 13 - dynamic programming applications
		To use dynamic programming, the problem must observe the principle of optimality, that whatever the initial state is, remaining decisions must be optimal with regard the state following from the first decision.
		Dynamic programming computes recurrences efficiently by storing partial results.
		Dynamic programming works best on objects which are linearly ordered and cannot be rearranged - characters in a string, matrices in a chain, points around the boundary of a polygon, the left-to-right order of leaves in a search tree.
	www.cs.sunysb.edu /~algorith/lectures-good/node13.html (770 words)

	Dynamic Net's Programming Portfolio
		The system also allows CEO to implement courses with unique features for their clients, who are identified as distinct Institutes on the system.
		Any number of courses or programs (group of courses) can be defined under an Institute, and the system provides a great deal of flexibility for clients who want an online presence for their courses.
		The programs were written to handle all of the data in a generic way so that no hard coding takes place, and the entire system is database driven.
	www.dynamicnet.net /services/portfolio/programming.htm (1392 words)

	Some Dynamic Programming Examples
		Tbis is very unusual for dynamic programming, and is really because this was quite a simple problem, but it does illustrate quite well the power of this method, and the things you have to think about when designing a dynamic programming algorithm.
		The dynamic programming table this time is two dimensional.
		There is a very simple algorithm, nothing to do with dynamic programming, that always seems to work perfectly, but doesn't.
	rabbit.eng.miami.edu /class/een512/dp.html (2259 words)

	Systematic Dynamic Programming in Bioinformatics
		Dynamic programming (DP) is a most fundamental programming technique in bioinformatics.
		The discipline is a program development method, applicable to a wide and well-defined class of sequence analysis problems.
		Dynamic Programming in the new framework looks and feels radically different from what we find in the textbooks.
	www.iscb.org /ismb2000/tutorials/evers.html (522 words)

	4. Dynamic Programming
		The term dynamic programming (DP) refers to a collection of algorithms that can be used to compute optimal policies given a perfect model of the environment as a Markov decision process (MDP).
		Classical DP algorithms are of limited utility in reinforcement learning both because of their assumption of a perfect model and because of their great computational expense, but they are still important theoretically.
		As we shall see, DP algorithms are obtained by turning Bellman equations such as these into assignments, that is, into update rules for improving approximations of the desired value functions.
	www.cs.ualberta.ca /~sutton/book/ebook/node40.html (323 words)

	Paul Vick and Erik Meijer - Dynamic Programming in Visual Basic
		Turning Option Strict Off lets you do dynamic programming, but you lose the benefits of compilation, taking performance hits (runtime type resolution) and reducing the ability of the compiler to detect coding errors.
		But for the interview, the goal was to educate views on what dynamic programming is, what the benefits are, and why developers should care - all in the context of Visual Basic today and tomorrow.
		If someone has experience or knowledge of dynamic programming already, then they may be a little frustrated with the introduction level questions asked.
	channel9.msdn.com /showpost.aspx?postid=116702 (2268 words)

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