Graphical algorithm for the knapsack problems

  • Authors:

  • Alexander Lazarev;Anton Salnikov;Anton Baranov

  • Affiliations:

  • Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia and Lomonosov Moscow State University, Higher School of Economics, Moscow Institute of Physics and Technology;Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia and Lomonosov Moscow State University, Higher School of Economics, Moscow Institute of Physics and Technology;Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia and Lomonosov Moscow State University, Higher School of Economics, Moscow Institute of Physics and Technology

  • Venue:
  • PaCT'11 Proceedings of the 11th international conference on Parallel computing technologies
  • Year:
  • 2011

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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 pj ≃ kwj for all j, where pj and wj are utility and capacity of item j = 1, 2,..., n.