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  2. Continuous knapsack problem - Wikipedia

    en.wikipedia.org/wiki/Continuous_knapsack_problem

    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.

  3. List of knapsack problems - Wikipedia

    en.wikipedia.org/wiki/List_of_knapsack_problems

    The knapsack problem is one of the most studied problems in combinatorial optimization, with many real-life applications. For this reason, many special cases and generalizations have been examined. For this reason, many special cases and generalizations have been examined.

  4. Knapsack problem - Wikipedia

    en.wikipedia.org/wiki/Knapsack_problem

    A 1999 study of the Stony Brook University Algorithm Repository showed that, out of 75 algorithmic problems related to the field of combinatorial algorithms and algorithm engineering, the knapsack problem was the 19th most popular and the third most needed after suffix trees and the bin packing problem.

  5. Bin packing problem - Wikipedia

    en.wikipedia.org/wiki/Bin_packing_problem

    The problem of fractional knapsack with penalties was introduced by Malaguti, Monaci, Paronuzzi and Pferschy. [44] They developed an FPTAS and a dynamic program for the problem, and they showed an extensive computational study comparing the performance of their models.

  6. Packing problems - Wikipedia

    en.wikipedia.org/wiki/Packing_problems

    de Bruijn's theorem: A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p, q, r (i.e., the box is a multiple of the brick.) [15]

  7. Configuration linear program - Wikipedia

    en.wikipedia.org/wiki/Configuration_linear_program

    Denote by C the set of different configurations (and their number). For each size s in S and configuration c in C, denote: n s - the number of items of size s. a s,c - the number of occurrences of size s in configuration c. x c - a variable denoting the number of bins with configuration c. Then, the configuration LP of bin-packing is:

  8. Karmarkar–Karp bin packing algorithms - Wikipedia

    en.wikipedia.org/wiki/Karmarkar–Karp_bin...

    The knapsack problem can be solved by dynamic programming in pseudo-polynomial time: (), where m is the number of inputs and V is the number of different possible values. To get a polynomial-time algorithm, we can solve the knapsack problem approximately, using input rounding.

  9. Cutting stock problem - Wikipedia

    en.wikipedia.org/wiki/Cutting_stock_problem

    For the one-dimensional case, the new patterns are introduced by solving an auxiliary optimization problem called the knapsack problem, using dual variable information from the linear program. The knapsack problem has well-known methods to solve it, such as branch and bound and dynamic programming. The Delayed Column Generation method can be ...