GPU-Based Influence Regions Optimization

  • Marta Fort
  • J. Antoni Sellarès
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7333)

Abstract

In this paper we introduce an optimization problem, that arises in the competitive facility location area, which involves the maximization of the weighted area of the region where a new facility has influence. We consider a finite set of points S in a bounded polygonal region domain D subdivided into several non-negative weighted regions according to a weighted domain partition \(\mathcal{P}\). For each point in S we define its k-nearest/farthest neighbor influence region as the region containing all the points of D having the considered point as one of their k-nearest/farthest neighbors in S. We want to find a new point s in D whose k-influence region is maximal in terms of weighted area according to the weighted partition \(\mathcal{P}\). We present a GPU parallel approach, designed under CUDA architecture, for approximately solving the problem and we also provide experimental results showing the efficiency and scalability of the approach.

Keywords

Grid Point Graphic Processing Unit Voronoi Diagram Atomic Function Global Memory 
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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References

  1. 1.
    Cabello, S., Díaz-Báñez, J.M., Langerman, S., Seara, C., Ventura, I.: Facility location problems in the plane based on reverse nearest neighbor queries. European Journal of Operational Research 202(1), 99–106 (2009)CrossRefGoogle Scholar
  2. 2.
    Cheong, O., Efrat, A., Har-Peled, S.: Finding a guard that sees most and a shop that sells most. Discrete Comput. Geom. 37(4), 545–563 (2007)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Dehne, F.K.H.A., Klein, R., Seidel, R.: Maximizing a Voronoi region: the convex case. Int. J. Comput. Geometry Appl. 15(5), 463–476 (2005)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Denny, M.: Solving geometric optimization problems using graphics hardware. Comput. Graph. Forum 22(3), 441–452 (2003)CrossRefGoogle Scholar
  5. 5.
    Drezner, Z., Hamacher, H.W.: Facility location - applications and theory. Springer (2002)Google Scholar
  6. 6.
    Eiselt, H.A., Laporte, G., Thisse, J.F.: Competitive location models: A framework and bibliography. Transportation Science 27, 44–54 (1993)MATHCrossRefGoogle Scholar
  7. 7.
    Fort, M., Sellarès, J.A.: A parallel GPU-based approach for solving multiple proximity queries in 2d and 3d euclidean spaces (submitted)Google Scholar
  8. 8.
    Lee, D.-T.: On k-nearest neighbor Voronoi diagrams in the plane. IEEE Transactions on Computers 31(6), 478–487 (1982)MATHCrossRefGoogle Scholar
  9. 9.
    Lieberman, M.D., Sankaranarayanan, J., Samet, H.: A Fast Similarity Join Algorithm Using Graphics Processing Units. In: International Conference on Data Engineering, pp. 1111–1120 (2008)Google Scholar
  10. 10.
    Nickel, S., Puerto, J.: Location theory - a unified approach. Mathematical Methods of Operations Research 66(2), 369–371 (2009)Google Scholar
  11. 11.
    Owens, J.D., Luebke, D., Govindaraju, N., Harris, M., Krüger, J., Lefohn, A.E., Purcell, T.J.: A survey of general-purpose computation on graphics hardware. Computer Graphics Forum 26(1), 80–113 (2007)CrossRefGoogle Scholar
  12. 12.
    Plastria, F.: Static competitive location: an overview of optimisation approaches. European Journal of Operational Research 129, 461–470 (2001)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Sengupta, S., Harris, M., Garland, M.: Efficient Parallel Scan Algorithms for GPUs. NVIDIA Technical Report NVR-2008-003 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marta Fort
    • 1
  • J. Antoni Sellarès
    • 1
  1. 1.Dept. Informàtica i Matemàtica AplicadaUniversitat de GironaSpain

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