The Subset Sum Problem

Hans Kellerer (), Ulrich Pferschy () and David Pisinger ()
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Hans Kellerer: University of Graz, Department of Statistics and Operations Research
Ulrich Pferschy: University of Graz, Department of Statistics and Operations Research
David Pisinger: University of Copenhagen, DIKU, Department of Computer Science

Chapter 4 in Knapsack Problems, 2004, pp 73-115 from Springer

Abstract: Abstract Given a set N = {1,..., n} of n items with positive integer weights w 1,..., w n and a capacity c, the subset sum problem (SSP) is to find a subset of N such that the corresponding total weight is maximized without exceeding the capacity c. Recall the formal definition as introduced in Section 1.2: (4.1) $$ (SSP)\,\max {\rm{imize}}\;\sum\limits_{j = 1}^n {{w_j}{x_j}} $$ (4.2) $$ {\rm{subject}}\;{\rm{to}}\;\sum\limits_{j = 1}^n {{w_j}{x_j}} \le c,$$ (4.3) $$ {x_j} \in \left\{ {0,1} \right\},\;j = 1,...,n.$$

Keywords: Dynamic Programming; Knapsack Problem; Dynamic Programming Algorithm; Polynomial Time Approximation Scheme; Large Item (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-540-24777-7_4

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