In theoretical computer science, the continuous knapsack problem (also known as the fractional knapsack problem) is an algorithmic problem in combinatorial optimization in which the goal is to fill a container (the "knapsack") with fractional amounts of different materials chosen to maximize the value of the selected materials.[1][2] It resembles the classic knapsack problem, in which the items to be placed in the container are indivisible; however, the continuous knapsack problem may be solved in polynomial time whereas the classic knapsack problem is NP-hard.[1] It is a classic example of how a seemingly small change in the formulation of a problem can have a large impact on its computational complexity.
^ abGoodrich, Michael T.; Tamassia, Roberto (2002), "5.1.1 The Fractional Knapsack Problem", Algorithm Design: Foundations, Analysis, and Internet Examples, John Wiley & Sons, pp. 259–260.
^Korte, Bernhard; Vygen, Jens (2012), "17.1 Fractional Knapsack and Weighted Median", Combinatorial Optimization: Theory and Algorithms, Algorithms and Combinatorics, vol. 21, Springer, pp. 459–461, ISBN 9783642244889.
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theoretical computer science, the continuousknapsackproblem (also known as the fractional knapsackproblem) is an algorithmic problem in combinatorial optimization...
The knapsackproblem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items...
The quadratic knapsackproblem (QKP), first introduced in 19th century, is an extension of knapsackproblem that allows for quadratic terms in the objective...
maximizing the value of items that can fit in the bin is known as the knapsackproblem. A variant of bin packing that occurs in practice is when items can...
NP-hard problem reducible to the knapsackproblem. The problem can be formulated as an integer linear programming problem. A paper machine can produce an...
optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsackproblem. In many such problems, such...
written that solve the problem in reasonable times in most cases. Similarly, algorithms can solve the NP-complete knapsackproblem over a wide range of...
have practical value for many hard problems. One of the examples of an approximate algorithm is the Knapsackproblem, where there is a set of given items...
known as submodular optimization subject to submodular cover or submodular knapsack constraint) admits bounded approximation guarantees. Partitioning data...
always problem-dependent. For instance, in the knapsackproblem one wants to maximize the total value of objects that can be put in a knapsack of some...
applications Design problems in communication Location problems Data mining Graph problemsKnapsack and packing problems Mixed integer problems Time tabling...
partition problem (WCGTPP) Arc-weighted l-cardinality tree problem (AWlCTP) Multiple knapsackproblem (MKP) Maximum independent set problem (MIS) Ant...
include: Problems in combinatorial optimization, such as: The vehicle routing problem, a form of shortest path problem The knapsackproblem: Given a set...
Algorithms. 12 (2): 34. arXiv:1709.03489. doi:10.3390/a12020034. ISSN 1999-4893. Implementation of the QAOA algorithm for the knapsackproblem with Classiq...
Konno; E. Zemel (1991). A Linear Time Algorithm for Solving Continuous Maximin KnapsackProblems. Vol. 10. O.R. Letters. pp. 23, 27. Megiddo, N.; A. Tamir;...
cipher Exponentiating by squaring Knapsackproblem Shor's algorithm Standard Model Symmetry in physics Burnside's problem Classification of finite simple...
Equity (economics) International trade Justice (economics) Knapsackproblem List of unsolved problems in fair division Nash bargaining game Pizza theorem Price...
this way, DFSS is closely related to operations research (solving the knapsackproblem), workflow balancing. DFSS is largely a design activity requiring tools...
allocation is a kind of the fair division problem in which the items to divide are discrete rather than continuous. The items have to be divided among several...
Dantzig–Wolfe decomposition Knapsackproblem Maximum flow problem Optimization (mathematics) Travelling salesman problem Shadow price List of Jewish American...
voting, finding a utilitarian budget-allocation requires solving a knapsackproblem. It is NP-hard, but can be solved reasonably fast in practice. There...
1998). "An improved genetic algorithm for the multiconstrained 0-1 knapsackproblem". 1998 IEEE International Conference on Evolutionary Computation Proceedings...
classical NP problems. To cite some of them: graph partitioning, multidimensional knapsack, travelling salesman problem, quadratic assignment problem, set cover...
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