Knapsack problem

Definition

The knapsack problem is the following problem in combinatorial optimization:Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

Related concepts

Affine function Approximation algorithm Baby-step giant-step Big O notation Bin packing problem Binary search Branch and bound Change-making problem Co-NP-complete Combinatorial auction Combinatorial optimization Continuous knapsack problem Cryptography Cutting stock problem David S. Johnson Decision problem Decision tree model Deterministic algorithm Dominance relations Dynamic programming EPTAS Empty set Fixed-point arithmetic Fixed investment Fully polynomial time approximation scheme Gekko (optimization software)George Dantzig Greatest common divisor Greedy algorithm Hadas Shachnai Hamiltonian (quantum mechanics)Hybrid algorithm Karp's 21 NP-complete problems Knapsack Knapsack auction Knapsack cryptosystems Linear programming relaxation List of knapsack problems Meet-in-the-middle attack Merkle–Hellman knapsack cryptosystem Michael R. Garey Multiple knapsack problem NP-complete P versus NP problem Packing problem Parallel computing Polynomial-time approximation scheme Portfolio (finance)Pseudo-polynomial time Pseudocode Pseudopolynomial Public-key cryptography Quadratic knapsack problem Quantum approximate optimization algorithm Quantum computation Randomized algorithm Rationals Real RAM Real number Resource allocation Rosetta Code Sartaj Sahni Securitization Strongly NP-complete Subset sum problem Suffix tree Turing machine Weak NP-completeness Weakly NP-complete Zvi Galil

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