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A Heuristic Method for Balanced Graph Partitioning: An Application for the Demarcation of Preventive Police Patrol Areas

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 5290)

Abstract

In this paper we describe a heuristic method, based on graph-partitioning algorithms, with the purpose of improving the demarcation of areas for police patrolling. This demarcation seeks to homogenize the number of crimes among the patrol regions. If the map of a particular region is taken as a graph, we can say that the problem faced by police forces (typically preventive police) is similar to the problem of finding balanced connected q partitions of graphs (BCPq). Since this is a problem belonging to the NP-Hard class, approximate algorithms are the most suitable for solving such a problem. The method described in this article obtains results nearest those considered optimal for the more general case of BCPq, for q ≥ 2.

Keywords

  • approximate algorithm
  • graphs
  • heuristic method
  • balanced connected partition

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References

  1. Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Sys. Tech. J., 291–307 (1970)

    Google Scholar 

  2. Fiduccia, C.M., Matteyses, R.M.: A linear time heuristic for improving network partitions. In: 19th Design Automaton Conference, pp. 175–181 (1982)

    Google Scholar 

  3. Chlebíková, J.: Approximating the maximally balanced connected partition problem in graphs. Information Processing Letters 60, 225–230 (1996)

    CrossRef  MathSciNet  Google Scholar 

  4. Chataigner, F., Salgado, L.R.B., Wakabayashi, Y.: Approximability and inaproximability results on balanced connected partitions of graphs. Discrete Mathematics and Theoretical Computer Science (DMTCS) 9, 177–192 (2007)

    MATH  MathSciNet  Google Scholar 

  5. Lucindo, R.P.F.L.: Partição de Grafos em Subgrafos Conexos Balanceados. Dissertação de mestrado, Universidade de São Paulo (2007)

    Google Scholar 

  6. Heath, M.T., Raghavan, P.: A Cartesian Parallel Nested Dissection Algorithm. SIAM Journal on Matrix Analysis and Applications (1994)

    Google Scholar 

  7. Pereira, M.R.: Particionamento Automático de Restrições. Tese de Doutorado, Universidade Federal do Rio de Janeiro (COPPE) (2006)

    Google Scholar 

  8. Karypis, G., Kumar, V.: A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. Technical Report TR 95-035. Departament of Computer Science. University of Minnesota (1995)

    Google Scholar 

  9. Salgado, L.R.B.: Algoritmos de Aproximação para Partições Conexas em Grafos. Tese de doutorado, Universidade de São Paulo (2004)

    Google Scholar 

  10. Moretti, C.O., Bittencourt, T.N., André, J.C., Martha, L.F.: Algoritmos Automáticos de Partição de Domínio. Escola Politécnica da Universidade de São Paulo, Boletim Técnico, BT/PEF-9803 (1998) ISSN 0103-9822

    Google Scholar 

  11. Simon, H.D., Teng, S.H.: Partitioning of Unstructured Problems for Parallel Processing. Computing Systems in Engineering 2, 135–148 (1991)

    CrossRef  Google Scholar 

  12. Gersting, J.L.: Mathematical Structures for Computer Science, 6th edn. W.H. Freeman, New York (2006)

    Google Scholar 

  13. Jung. Java Universal Network/Graph Framework (2003) (Last access: February 14 , 2008), http://jung.sourceforge.net/index.html

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Assunção, T., Furtado, V. (2008). A Heuristic Method for Balanced Graph Partitioning: An Application for the Demarcation of Preventive Police Patrol Areas. In: Geffner, H., Prada, R., Machado Alexandre, I., David, N. (eds) Advances in Artificial Intelligence – IBERAMIA 2008. IBERAMIA 2008. Lecture Notes in Computer Science(), vol 5290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88309-8_7

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  • DOI: https://doi.org/10.1007/978-3-540-88309-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88308-1

  • Online ISBN: 978-3-540-88309-8

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