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

Assure Lution Poss 

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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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