A Genetic Algorithm to Partition Weighted Planar Graphs in Which the Weight of Nodes Follows a Power Law

  • Rodrigo Palheta
  • Vasco Furtado
Part of the Studies in Computational Intelligence book series (SCI, volume 424)


This research makes use of evidence that the distribution of crime by census tracts in large cities follows a Power Law. This means that there are few places that concentrate many crimes and many places that concentrate few crimes. In this article we investigate how modeling complex networks and genetic algorithms can help to understand the behavior of samples representing views of part of the map of crimes of a large metropolis. The representation of the network is a planar graph where the nodes are the centroids of census tracts, the edges represent the adjacency between the tracts, and each node has a weight representing the number of crimes recorded in the census tract. The problem of this research lies in the context of the study of sampling distributions that have long tails (e.g. the weight of the nodes of the graph follows a Power Law). In particular, we describe a genetic algorithm to explore the space of possible samples of the initial distribution (plotted crimes throughout the city) so that the maximum number of samples holds features to follow a Power Law with an exponent close to the original distribution.


Genetic Algorithm Initial Population Planar Graph Census Tract Span Minimum Tree 
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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  1. Cançado, T.: Alocação e despacho de recursos para o combate à criminalidade. Dissertação de mestrado, Departamento de Ciência da Computação, UFMG (2005)Google Scholar
  2. Clauset, A., Moore, C.: Accuracy and Scaling Phenomena in Internet Mapping. Phys. Rev. Lett. 94(1), 018701 (2005)CrossRefGoogle Scholar
  3. Cole, R.M.: Clustring with Genetic Algorithms. Master’s thesis, Department of Computer Science, University of Western Australia (1998)Google Scholar
  4. Datta, D., Figueira, J.R., Fonseca, C.M., Tavares-Pereira, F.: Graph Partitioning Through a Multi-Objective Evolutionary Algorithm: A Preliminary Study. In: Keijzer, M. (ed.) Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation (GECCO 2008), pp. 625–632. ACM, New York (2008)CrossRefGoogle Scholar
  5. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2) (2002)Google Scholar
  6. Devroye, L.: Non-Uniform Random Variate Generation. Springer, New York (1986)zbMATHGoogle Scholar
  7. Erdős, P., Rényi, A.: On Random Graphs I in Publ. Math. Debrecen 6, 290–297 (1959)Google Scholar
  8. Furtado, V., Ayres, L., de Oliveira, M., Vasconcelos, E., Caminha, C., D’Orleans, J.: Collective In telligence in Law Enforcement: The WikiCrimes System. Information Science 180 (2010)Google Scholar
  9. Gatterbauer, W.: Rules of Thumb for Information Acquisition from Large and Redundant Data. In: Clough, P., Foley, C., Gurrin, C., Jones, G.J.F., Kraaij, W., Lee, H., Mudoch, V. (eds.) ECIR 2011. LNCS, vol. 6611, pp. 479–490. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. McLafferty, S.: Identification, development and implementation of innovative crime mapping techniques and spatial analysis, p. 27. U.S. Department of Justice, Washington, D.C (2000)Google Scholar
  11. Melo, A.: Um modelo multiagente de simulação criminal bio-inspirado. Dissertação de mestra do, Mestrado em Informática Aplicada. In: UNIFOR (2008)Google Scholar
  12. Pickering, G., Bull, J.M., Sanderson, D.J.: Sampling Power-law Distributions. Tectonophysics 248, 1–20 (1995)CrossRefGoogle Scholar
  13. Semaan, G.S., Brito, J.A.M., Ochi, L.S.: Um algoritmo evolutivo híbrido aplicado ao problema de clusterização em grafos com restrições de capacidade e contiguidade. In: Anais do IX Congresso Brasileiro de Redes Neurais e Inteligência Computacional (IX CBRN), Ouro Preto/MG (2009)Google Scholar
  14. Stumpf, M., Wiuf, C., May, R.: Subnets of scale-free networks are not scale-free: Sampling properties of networks. PNAS,102 (March 22, 2005)Google Scholar
  15. Tavares-Pereira, F., Figueira, J.R., Mousseau, V., Roy, B.: Multiple criteria districting problems: The public transportation network pricing system of the Paris region. Annals of Operations Research 154(1), 69–92 (2007)MathSciNetzbMATHCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of FortalezaFortalezaBrazil

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