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Topic: Greedy algorithm

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	Pattern for Greedy Algorithms
		Greedy algorithm always makes the choice that looks best at the moment (local optimal choice), in hopes that this choice will lead to a global optimal solution.
		Greedy algorithms, just as in real life, provide immediate “best” and shortsighted choice on the basis of information available at hand without worrying about the effects of these decisions may have in future.
		Greedy algorithms do not always yield optimal solutions because at some iteration that looks to be locally optimal may not be globally optimal.
	www.scs.carleton.ca /~tpathman/GreedyAlgorithmPattern.htm (2140 words)

	DIGITAL VIDEO: COMPRESSION: BMAs: Greedy Algorithms
		Greedy algorithms attempt to reduce the number of matching criteria evaluations by shifting the centre of a search pattern immediately on finding a vector with a distortion lower than the current centre.
		Greedy algorithms are less ambitious than non-greedy algorithms in that they continuously look for a better position rather than the best position.
		Greedy Algorithm B is similar to Algorithm A, except that at the initial step size is one quarter (s := d div 4) of the maximum permissible displacement.
	www.newmediarepublic.com /dvideo/compression/adv18.html (992 words)

	Greedy Algorithms
		A greedy algorithm repeatedly executes a procedure which tries to maximize the return based on examining local conditions, with the hope that the outcome will lead to a desired outcome for the global problem.
		A greedy algorithm may at each stage employ the criteria of providing the largest available coin which is not greater than the amount still owed.
		A greedy algorithm, for finding such a representation, can at each stage add to the sum the largest unit fraction which does not cause the sum to exceed the fraction.
	www.cse.ohio-state.edu /~gurari/course/cis680/cis680Ch17.html (583 words)

	Class 1: Introduction
		A greedy algorithm always makes a choice that is locally optimal in the hope that it will lead to a globally optimal solution.
		Demonstrate that, having made the greedy choice, what remains is a subproblem with the property that if we combine an optimal solution to the subproblem with the greedy choice that we have made, we arrive at an optimal solution to the original problem.
		Huffman's greedy algorithm uses a table of frequencies of occurrence of the characters to build up an optimal way to represent each character as a binary string.
	cs.gmu.edu /syllabus/syllabi-fall03/cs483-kaznachey/12/GreedyAlgorithms.htm (1068 words)

	greedy algorithm (Site not responding. Last check: 2007-10-19)
		Greedy algorithms find the overall, or globally, optimal solution for some optimization problems, but may find less-than-optimal solutions for some instances of other problems.
		In contrast, any known greedy algorithm to find a Hamiltonian cycle might not find the shortest path, that is, a solution to the traveling salesman problem.
		Greedy algorithms are usually quicker, since they don't consider the details of possible alternatives.
	www.nist.gov /dads/HTML/greedyalgo.html (195 words)

	IBM RD 50-1 \| An approximation to the greedy algorithm for differential compression
		It is an approximation of the quadratic-time linear-space greedy algorithm [1].
		Their one-pass differencing algorithm has been proven to be linear in the worst case but to produce suboptimal compression, since it neither detects transpositions in data nor finds optimal matches at a given location of the version file.
		The main data structures in the algorithm that require space proportional to the number of blocks in the reference file are the hash value array, the suffix array, the rank array in the suffix array construction routine, the quick index array, the pointer array, and the block hash table.
	www.research.ibm.com /journal/rd/501/agarwal.html (10710 words)

	Algorithm - DmWiki
		Advance simply continues execution of the algorithm at the next instruction in the algorithm, while jump continues the algorithm at the passed position.
		When talking about algorithms there are a few standard terms that describe the strategy an algorithm uses to solve a problem.
		Greedy algorithms try to solve a problem by applying tactics that solve a problem in the best way locally.
	www.devmaster.net /wiki/Algorithm (799 words)

	CMSC 435 Algorithm Analysis & Design
		Greedy algorithms are often employed in optimization problems where it can be proved that a greedy choice selection results in an optimal solution to the given problem.
		Kruskal's minimum spanning tree algorithm is a particular case of the general greedy algorithm shown above.
		To implement the union-find algorithm we construct two arrays -- one labeled parent and the other labeled rank, The rank array is initiallized to 0 and the parent[i] = i for all i = 0 to V For each equivalence class, one of the vertices serves as a label or a root for that class.
	www.academic.marist.edu /jte/algorithms/Greedy.htm (1469 words)

	The Greedy Algorithm for Unit Fractions)
		If we apply the "greedy algorithm", which consists of taking the largest qualifying unit fraction at each stage, we would begin with the term 1/3, leaving a remainder of 1/3.
		So,the odd greedy expansion of 2/3 terminates after four steps, giving the result 2/3 = 1/3 + 1/5 + 1/9 + 1/45 The non-zero remainders we encountered during this process were 1/3, 2/15, and 1/45, with the numerators 1, 2, 1.
		This is not a trivial question, as shown by the odd greedy expansion of 1 (not using 1/1 on the first step).
	www.mathpages.com /home/kmath454.htm (1049 words)

	Greedy algorithm for Egyptian fractions - Wikipedia, the free encyclopedia
		It is called a greedy algorithm because at each step the algorithm chooses greedily the largest possible unit fraction that can be used in any representation of the remaining fraction.
		Stratemeyer (1930) and Salzer (1947) describe a method of finding an accurate approximation for the roots of a polynomial, by applying the greedy algorithm to compute the greedy expansion of the root, at each step maintaining a polynomial the root of which is the remaining fraction to be expanded.
		The length, minimum denominator, and maximum denominator of the greedy expansion for all fractions with small numerators and denominators can be found in the On-Line Encyclopedia of Integer Sequences as sequences A050205, A050206, and A050210, respectively.
	en.wikipedia.org /wiki/Greedy_algorithm_for_Egyptian_fractions (1279 words)

	[No title]
		The greedy algorithm is to keep on giving as many coins of the largest denomination until you the value that remains to be given is less than the value of that denomination.
		Now, notice that the greedy algorithm leads to a combination that always maps one coin to one or more coins in other combinations and NEVER maps more than one coin to a single coin in another combination.
		Thus, the number of coins given by the greedy algorithm is minimal.
	www.cs.ucf.edu /~dmarino/ucf/cop3530/lectures/COP3530Greedy01.doc (626 words)

	Greedy algorithm - Wikipedia, the free encyclopedia
		A greedy algorithm is an algorithm that follows the problem solving metaheuristic of making the locally optimum choice at each stage with the hope of finding the global optimum.
		If a greedy algorithm can be proven to yield the global optimum for a given problem class, it typically becomes the method of choice because it is faster than other optimisation methods like dynamic programming.
		Examples of such greedy algorithms are Kruskal's algorithm, Dijkstra's algorithms for finding Single-Source Shortest paths and Prim's algorithm for finding minimum spanning trees and the algorithm for finding optimum Huffman trees.
	en.wikipedia.org /wiki/Greedy_algorithm (606 words)

	McGill University School of Computer Science: CS203A
		In the algorithm, we progressively construct a spanning tree of the graph such that, if v is the vertex the algorithm starts with, then the spanning tree is simply the union of shortest paths from v to all other vertices in the graph.
		The greedy choice in Dijkstra's algorithm is then to choose the vertex not in the tree with the smallest known distance from v.
		When the algorithm finishes, we want d(u) to be equal to d(v,u), the length of the actual shortest path from v to u.
	cgm.cs.mcgill.ca /~msuder/courses/203/lectures/greedy_algorithms (1616 words)

	The Greedy Method (Site not responding. Last check: 2007-10-19)
		To sort using the greedy method, have the selection policy select the minimum of the remaining input.
		Method (the Greedy method): The selection policy (of which best pair of arrays to merge next) is to choose the two shortest remaining arrays.
		Greedy selection policy: choose from all the nodes still outside Y the node of minimum DIST value, and add it to Y. The claim, which will proved later, is that every node in Y has is DIST value equal to the distance from it to s.
	www.mutah.edu.jo /userhomepages/CS252/greedy.html (1367 words)

	Algorithm Design Paradigms - Greedy Method
		Even for problems which can be solved exactly by a greedy algorithm, establishing the correctness of the method may be a non-trivial process.
		Greedy methods are distinguished by the fact that the selection function assigns a numerical value to each candidate, x, and chooses that candidate for which:
		A Greedy Algorithm for a particular problem is specified by describing the predicates `solution' and `feasible'; and the selection function `select'.
	www.csc.liv.ac.uk /~ped/teachadmin/algor/greedy.html (1235 words)

	Algorithm Tutorials (Site not responding. Last check: 2007-10-19)
		As a greedy man takes as much as he can as often as he can, in our case we are choosing at every step the activity that finishes first and do so every time there is no activity in progress.
		The greedy algorithms we have seen so far work well in every possible situation as their correction has been proven.
		Such an algorithm is not very hard to come with and after a short analysis we notice that in order to maximize the total number of groups it is always optimal to form a group from the k countries that have the highest number of citizens.
	www.topcoder.com /tc?module=Static&d1=tutorials&d2=greedyAlg (4535 words)

	Greedy algorithm
		The greedy algorithm gives (5, 1, 1, 1) but (4, 4) is better.
		It shows that it can be decided in polynomial time (O(n^2)) if a certain combination of coin values can always be solved optimally with the greedy algorithm, even though determining the least number of coins needed for a given set of coin values and total x is NP-hard.
		Not all superincreasing sequences are solved optimally by the greedy algorithm; consider coins {2001, 1000, 1} and total 3000.
	www.physicsforums.com /showthread.php?threadid=134752 (484 words)

	CMSC 435 Algorithm Analysis & Design
		Write a greedy algorithm for assigning each of the n tasks to n time slots so that the total penalty incurred is a minimum.
		Construct and implement efficient algorithms (with the same compiler) of Prim’s and Kruskal’s algorithms to find the minimum spanning tree (MST) for the graph included with this assignment.
		Your output should consist of a list of edges in each of the trees, and you may also choose to color these edges on a copy of the graph that you have received.
	www.academic.marist.edu /~jzbv/algorithms/GreedyPrimKruskal.htm (512 words)

	CSC-223 97F : Greedy Algorithms
		A greedy algorithm assumes that a local optimimum is part of the global optimimum.
		The principal advantage of greedy algorithms is that they are usually straightforward, easy to understand and easy to code.
		The greedy policy of taking as many as possible of those items may leave an empty space in the bag, too small to accommodate any of the items left in the warehouse, but large enough that the overall value density is well below that of other items.
	www.math.grin.edu /~rebelsky/Courses/223/97F/Readings/greedy.html (1148 words)

	greedy algorithm (Site not responding. Last check: 2007-10-19)
		Note: Prim's algorithm and Kruskal's algorithm are greedy algorithms that find the globally optimal solution, a minimum spanning tree.
		In contrast, any known greedy algorithm to find an Hamiltonian cycle might not find the shortest path, that is, a solution to the traveling salesman problem.
		Dijkstra's algorithm for finding shortest paths, Huffman encoding and optimal merge are other examples of greedy algorithms that find optimal solutions.
	ce.sharif.edu /~ghodsi/ds-alg-dic/HTML/greedyalgo.html (183 words)

	Mazes
		The algorithms are greedy in that, on every iteration, out of the available set, they select an edge of the minimum weight.
		On every step of the algorithm we have a set of vertices connected by edges such that the graph they form is a tree.
		On every step of the algorithm we have a set of edges such that the graph they form is circuit-free.
	www.cut-the-knot.org /ctk/Mazes.shtml (1586 words)

	Greedy Algorithms (Site not responding. Last check: 2007-10-19)
		When the algorithm terminates, we hope that the local optimum is equal to the global optimum.
		If this is the case, then the algorithm is correct; otherwise, the algorithm has produced a suboptimal solution.
		If the best answer is not required, then simple greedy algorithms are sometimes used to generate approximate answers, rather than using the more complicated algorithms generally required to generate an exact answer."
	www.cs.man.ac.uk /~graham/cs2022/greedy (276 words)

	Ideas, Concepts and Definitions (Site not responding. Last check: 2007-10-19)
		The idea behind a greedy algorithm is to perform a single procedure in the recipe over and over again until it can't be done any more and see what kind of results it will produce.
		Map Coloring: There is no algorithm that will produce a minimal coloring (a coloring using the fewest number of colors) for every single map, but often you can get good results by choosing one color, and coloring as many regions as possible with that color before going on to another color.
		Each time that you use this greedy algorithm to find a dominating set, you will have to decide for yourself if you have found the smallest possible dominating set that can be found for that graph.
	www.c3.lanl.gov /mega-math/gloss/compute/greedy.html (434 words)

	3.2- Greedy algorithm for phylograph
		There is a natural greedy algorithm for the Minimum Phylograph problem.
		In a phylograph, every character's induced subgraph consists of a single connected component, so the greedy algorithm ``grows'' a solution by iteratively adding an edge that maximally reduces the number of connected components.
		The greedy algorithm begins with each species an isolated vertex, and iteratively adds the edge which maximally decreases the cost, until the cost is 0.
	www.research.ibm.com /antivirus/SciPapers/Sorkin/VIRALL/virall-node11.html (160 words)

	The Compact Tree Algorithm
		The Compact Tree (CT) algorithm for the problem is a greedy algorithm, which like Prim's algorithm for Minimum Spanning Tree[#!clr-algorithm!#], builds a spanning tree incrementally.
		In this case, the session request is simply rejected; The other case is that during the progression of the algorithm, a vertex with a degree constraint of one is added to the tree, when the sum of the spare degrees of the tree vertices is also one.
		We have shown that there can be no polynomial algorithm that approximates the problem to within a constant ratio.
	www.arl.wustl.edu /~sherlia/thesis/chap3/node4.html (444 words)

	Greedy - AOL Music
		The greedy algorithm determines the minimum amount of US coins to give while...
		Definition of greedy algorithm, possibly with links to more information and implementations.
		Download, listen and watch Greedy music, mp3's, song lyrics, music videos, Internet radio, live performances, concerts, and more on AOL Music.
	music.aol.com /artist/greedy/310006/main (104 words)

	Egyptian Fractions
		This algorithm simply adds to the sum so far the largest possible unit fraction which does not make the sume exceed the given fraction.
		Implement the Greedy Algorithm in a procedure which calculates the Egyptian representation of any function.
		The first input is a list of the fractions obtained so far by the Greedy Algorithm and the second variable is the fraction to be represented.
	www.math.yorku.ca /Who/Faculty/Steprans/Courses/2042/EgyptianFractions/EgyptianFractions.html (427 words)

	Greedy Algorithm
		This is a greedy strategy because once a coin has been counted out, it is never taken back.
		The greedy algorithm selects 15 followed by five ones--six coins in total.
		The solution found by the greedy strategy is a feasible solution, but it does not minimize the objective function.
	www.brpreiss.com /books/opus4/html/page444.html (233 words)

	Data Structures and Algorithms: Proving MST
		We choose the step that maximises the immediate gain (in the case of the minimum spanning tree - made the smallest possible addition to the total cost so far) without thought for the effect of this choice on the remainder of the problem.
		So the commonest method of proving a greedy algorithm is to use proof by contradiction, we show that if we didn't make the "greedy" choice, then, in the end, we will find that we should have made that choice.
		At each step in the MST algorithm, we choose the cheapest edge that would not create a cycle.
	www.oopweb.com /Algorithms/Documents/PLDS210/Volume/greedy_proof.html (337 words)

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