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Topic: Knapsack problem

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	knapsack problem
		Note: Also called 0-1 or binary knapsack (each item may be taken (1) or not (0)), in contrast to the fractional knapsack problem.
		Also called bounded knapsack (BKP) because there are a limited number of items, in contrast to the unbounded knapsack problem.
		The decision problem is, given items of different values and volumes and a knapsack, is there a subset that exceeds a certain value?
	www.nist.gov /dads/HTML/knapsackProblem.html (219 words)

	1.2.10 Knapsack Problem (Site not responding. Last check: )
		Problem: Find the subset S' \subset S which maximizes the value of \sum_{i \in S'} v_i given that \sum_{i \in S'} s_i \leq C, ie.
		The term knapsack problem invokes the image of the backbacker who is constrained by a fixed-size knapsack and so must fill it only with the most useful items.
		The typical formulation in practice is the 0/1 knapsack problem, where each item must be put entirely in the knapsack or not included at all.
	www.cs.sunysb.edu /~algorith/files/knapsack.shtml (299 words)

	Knapsack problem - Wikipedia, the free encyclopedia
		The knapsack problem is a problem in combinatorial optimization.
		Both the general knapsack problem and the subset sum problem are NP-hard, and this has led to attempts to use subset sum as the basis for public key cryptography systems, such as Merkle-Hellman.
		This does not contradict the fact that the knapsack problem is NP-complete, since C, unlike n, is not polynomial in the length of the input to the problem.
	en.wikipedia.org /wiki/Knapsack_problem (827 words)

	Knapsack problem at opensource encyclopedia (Site not responding. Last check: )
		The knapsack problem is a problem in complexity theory, cryptography, and applied mathematics.
		The 0/1 knapsack problem restricts the number of each items to zero or one.
		Merkle-Hellman and several similar algorithms were later broken, because the subset sum problems they produced were in fact solvable by polynomial-time algorithms.
	www.wiki.tatet.com /Knapsack_problem.html (342 words)

	GATE Study Material \| General Knapsack problem
		In a knapsack problem there is a knapsack or a container of capacity M n items where, each item i is of weight w
		The problem of knapsack is to fill the available items into the knapsack so that the knapsack gets filled up and yields a maximum profit.
		This type of knapsack problems is a general knapsack problem.
	www.onestopgate.com /gate-study-material/5.2.asp (261 words)

	Knapsack problem - Computing Reference - eLook.org
		Such constraint satisfaction problems are often solved using dynamic programming.
		The general knapsack problem is NP-hard, and this has led to attempts to use it as the basis for public-key encryption systems.
		Several such attempts failed because the knapsack problems they produced were in fact solvable by polynomial-time algorithms.
	www.elook.org /computing/knapsack-problem.htm (108 words)

	Knapsack Problem
		The typical formulation in practice is the 0/1 knapsack problem, where each item must be put entirely in the knapsack or not included at all.
		The constant `price-per-pound' knapsack problem is often called the subset sum problem, because given a set of numbers, we seek a subset that adds up to a specific target number, i.e.
		The first algorithm for generalized public key encryption by Merkle and Hellman [MH78] was based on the hardness of the knapsack problem.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE145.HTM (1194 words)

	Search Tuna Report for bin packing (Site not responding. Last check: )
		Note: A common form of the problem is, what is the least number of bins containers of fixed volume needed to hold a set of objects....
		Of these 720 problems, the optimal solution is known in 704 cases, and in the other sixteen, the optimal solution is known to lie in some interval of size 2 or 3....
		Similar problems concern cutting of pieces into particular smaller ones so as to minimize the wastage of material and scheduling of identical parallel processors so as to minimize the total completion time....
	www.searchtuna.com /ftlive2/3850.html (1542 words)

	The Knapsack Problem. (Site not responding. Last check: )
		The knapsack problem is a particular type of integer program with just one constraint.
		Each item that can go into the knapsack has a size and a benefit.
		As an example, suppose we have three items as shown in Table 4, and suppose the capacity of the knapsack is 5.
	mat.gsia.cmu.edu /classes/dynamic/node5.html (143 words)

	Dictionary of Algorithms and Data Structures
		This is a dictionary of algorithms, algorithmic techniques, data structures, archetypal problems, and related definitions.
		Data Structures and Algorithms is a wonderful site with illustrations, explanations, analysis, and code taking the student from arrays and lists through trees, graphs, and intractable problems.
		This dictionary is an example for Problem Set 4 of Software Engineering of Innovative Web Services.
	www.nist.gov /dads (686 words)

	Knapsack Problem
		If you have never heard about this problem (shame on you!) you might be interested in taking a quick look at the formal definition given below.
		The name derives from the following interpretation: suppose that you have a knapsack of volume U and you wish to fill it up with available items so as to maximize the total value of the items in the knapsack.
		Recall that, as indicated above, the "unbounded" version of the knapsack problem allows you to select as many items of each type as you wish, subject to the total volume constraint.
	www-cse.uta.edu /~holder/courses/cse2320/lectures/applets/knapsack/knapsack.html (384 words)

	General Knapsack problem - Study Notes
		In a knapsack problem there is a knapsack or a container of capacity M n items where, each item i is of weight w
		The problem of knapsack is to fill the available items into the knapsack so that the knapsack gets filled up and yields a maximum profit.
		This type of knapsack problems is a general knapsack problem.
	www.vyomworld.com /gate/cs/ada/5.2.asp (299 words)

	Knapsack Problem -- from Wolfram MathWorld
		This system relies on the existence of a class of knapsack problems which can be solved trivially (those in which the weights are separated such that they can be "peeled off" one at a time using a greedy-like algorithm), and transformations which convert the trivial problem to a difficult one and vice versa.
		The simple knapsack system was broken by Shamir in 1982, the Graham-Shamir system by Adleman, and the iterated knapsack by Ernie Brickell in 1984.
		Coppersmith, D. "Knapsack Used in Factoring." §4.6 in Open Problems in Communication and Computation (Ed.
	mathworld.wolfram.com /KnapsackProblem.html (181 words)

	The GA Playground: Weing1 - A Multiple 0/1 Knapsack Problem
		A multiple knapsack problem with 2 knapsacks and 28 objects
		A knapsack problem (see description in the Single Knapsack Problem file), where there are multiple knapsacks, and each object has a different weight for each knapsack.
		The problem map file (profit and weight values) is KnapsackWeing1.gmp
	www.aridolan.com /ofiles/ga/gaa/KnapsackWeing1.aspx (158 words)

	Design and Analysis of Computer Algorithms
		-- Blackbox is a planning system that works by converting problems specified in STRIPS notation into Boolean satisfiability problems, and then solving the problems with a variety of state-of-the-art satisfiability engines.
		-- This is a preliminary version of the catalog of NP optimization problems.
		One strong motivation for creating SATLIB is to provide a uniform test-bed for SAT solvers as well as a site for collecting SAT problem instances, algorithms, and empirical characterisations of the algorithms' performance.
	www.personal.kent.edu /~rmuhamma/Algorithms/algorithm.html (718 words)

	I have problem about Knapsack in ASM - Assembly
		You're currently browsing the Assembly section within the Software Development category of DaniWeb, a massive community of 174,705 software developers, web developers, Internet marketers, and tech gurus who are all enthusiastic about making contacts, networking, and learning from each other.
		I try to write about this problem but i can't...
		For small number of items, humans are preety good at solving this problem by inspection.
	www.daniweb.com /techtalkforums/post256373.html (360 words)

	The GA Playground: Weish01 - A Multiple 0/1 Knapsack Problem
		The GA Playground: Weish01 - A Multiple 0/1 Knapsack Problem
		A multiple knapsack problem with 5 knapsacks and 30 objects
		The problem map file (profit and weight values) is KnapsackWeish01.gmp
	www.aridolan.com /ofiles/ga/gaa/KnapsackWeish01.aspx (158 words)

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