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The Knapsack as a Nonlinear Function

  • Rainer A. Rueppel
Part of the Communications and Control Engineering Series book series (CCE)

Abstract

The classical knapsack problem (also referred to as subset problem or 0/1 knapsack problem) is the following: given a set of N weights wl, ..., wN and a “test” weight T, determine whether there exists a subset of weights which exactly sums to T. More formally, the 0/1 knapsack defines a function from the set of binary N-tuples into the nonnegative integers:
$${F_w}:{\left\{ {0,1} \right\}^N} \to {Z^ + }$$
(7.1a)
With
$$S = {F_W}\left( {\underline x } \right) = {x_1}{w_1} + \ldots + {x_N}{w_N} = \sum\limits_{j = 1}^N {{x_j}} {w_j}\,.$$
(7.1b)
.

Keywords

Polynomial Time Knapsack Problem Modular Transformation Deterministic Computer Integer Addition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin, Heidelberg 1986

Authors and Affiliations

  • Rainer A. Rueppel
    • 1
  1. 1.Dept. of Electrical Engineering and Computer ScienceUniversity of California, San DiegoLa JollaUSA

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