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Graphical Algorithm for the Knapsack Problems

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Parallel Computing Technologies (PaCT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6873))

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Abstract

We consider a modification of dynamic programming algorithm (DPA), which is called as graphical algorithm (GA). For the knapsack problem (KP) it is shown that the time complexity of GA is less than the time complexity of DPA. Moreover, the running time of GA is often essentially reduced. GA can also solve big scale instances and instances, where the parameters are not only positive integer. The paper outlines different methods of parallelizing GA taking into account its main features and advantages to various parallel architectures, in particular by using OpenCL and MPI framework. Experiments show that ”hard” instances of KP for GA have correlation p j  ≃ kw j for all j, where p j and w j are utility and capacity of item j = 1, 2, …, n.

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Author information

Authors and Affiliations

  1. Institute of Control Sciences of the Russian Academy of Sciences, Profsoyuznaya st. 65, 117997, Moscow, Russia

    Alexander Lazarev & Anton Salnikov

  2. Higher School of Economics, Lomonosov Moscow State University, State University, Russia

    Anton Baranov

  3. Moscow Institute of Physics and Technology, State University, Russia

    Anton Salnikov & Anton Baranov

Authors
  1. Alexander Lazarev
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  2. Anton Salnikov
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  3. Anton Baranov
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Editor information

Editors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Supercomputer Software Department, Russian Academy of Sciences Pr. Lavrentieva, ICM&MG RAS, 630090, Novosibirsk, Russia

    Victor Malyshkin

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© 2011 Springer-Verlag Berlin Heidelberg

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Lazarev, A., Salnikov, A., Baranov, A. (2011). Graphical Algorithm for the Knapsack Problems. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2011. Lecture Notes in Computer Science, vol 6873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23178-0_41

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  • DOI: https://doi.org/10.1007/978-3-642-23178-0_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23177-3

  • Online ISBN: 978-3-642-23178-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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