Detecting Hotspots in Geographic Networks

  • Kevin BuchinEmail author
  • Sergio Cabello
  • Joachim Gudmundsson
  • Maarten Löffler
  • Jun Luo
  • Günther Rote
  • Rodrigo I.Silveira
  • Bettina Speckmann
  • Thomas Wolle
Conference paper
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)

Abstract. We study a point pattern detection problem on networks, motivated by

geographical analysis tasks, such as crime hotspot detection. Given a network N (for example, a street, train, or highway network) together with a set of sites which are located on the network (for example, accident locations or crime scenes), we want to find a connected subnetwork F of N of small total length that contains many sites. That is, we are searching for a subnetwork F that spans a cluster of sites which are close with respect to the network distance.

We consider different variants of this problem where N is either a general graph or restricted to a tree, and the subnetwork F that we are looking for is either a simple path, a path with self-intersections at vertices, or a tree. Many of these variants are NP-hard, that is, polynomial-time solutions are very unlikely to exist. Hence we focus on exact algorithms for special cases and efficient algorithms for the general case under realistic input assumptions.


Tree Decomposition Simple Path Internal Vertex Orienteering Problem Partial Edge 
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. Aerts, K., Lathuy, C., Steenberghen, T., and Thomas, I. (2006). Spatial clustering of traffic accidents using distances along the network. In Proc. 19th Workshop Intern. Cooperation on Theories and Concepts in Traffic Safety.Google Scholar
  2. Arkin, E. M., Mitchell, J. S. B., and Narasimhan, G. (1998). Resource-constrained geometric network optimization. In Proc. 14th Symp. Computational Geometry, pages 307–316.Google Scholar
  3. Awerbuch, B., Azar, Y., Blum, A., and Vempala, S. (1998). New approximation guarantees for minimum-weight k-trees and prize-collecting salesmen. SIAM Journal on Computing, 28(1):254–262.CrossRefGoogle Scholar
  4. Beineke, L. W. and Pippert, R. R. (1971). The number of labeled dissections of a k-ball. Math. Ann., 191:87–98.CrossRefGoogle Scholar
  5. Bender, M. A., Farach-Colton, M., Pemmasani, G., Skiena, S. S., and Sumazin, P. (2005). Lowest common ancestors in trees and directed acyclic graphs. Journal of Algorithms, 57(2):75–94.CrossRefGoogle Scholar
  6. Blum, A., Chawla, S., Karger, D. R., Lane, T., Meyerson, A., and Minkoff, M. (2007). Approximation algorithms for orienteering and discounted-reward TSP. SIAM Journal on Computing, 37(2):653–670.CrossRefGoogle Scholar
  7. Bodlaender, H. (2007). Treewidth: Structure and algorithms. In Proc. 14th Colloquium on Structural Information and Communication Complexity, number 4474 in LNCS, pages 11–25.Google Scholar
  8. Celik, M., Shekhar, S., George, B., Rogers, J. P., and Shine, J. A. (2007). Discovering and quantifying mean streets: A summary of results. Technical Report 07–025, University of Minnesota -Comp. Science and Engineering.Google Scholar
  9. Chekuri, C., Korula, N., and P´al, M. (2008). Improved algorithms for Orienteering and related problems. In Proc. 19th ACM-SIAM Symp. Discrete Algorithms, pages 661–670.Google Scholar
  10. Chen, K. and Har-Peled., S. (2006). The orienteering problem in the plane revisited. In Proc. 22nd Symp. Computational Geometry, pages 247–254.Google Scholar
  11. Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C. (2001). Introduction to Algorithms. MIT Press and McGraw-Hill, 2nd edition.Google Scholar
  12. Fotheringham, S. and Rogerson, P. (1994). Spatial Analysis and GIS. Taylor and Francis, London.Google Scholar
  13. Golden, B., Levy, L., and Vohra, R. (1987). The orienteering problem. Naval Research Logistics, 34:307–318.CrossRefGoogle Scholar
  14. Illinois Criminal Justice Information Authority (1996). STAC user manual.Google Scholar
  15. Kloks, T. (1993). Treewidth. PhD thesis, Utrecht University.Google Scholar
  16. Levine, N. (2005). Crime mapping and the Crimestat program. Geographical Analysis, 38:41–56.CrossRefGoogle Scholar
  17. Miller, H. and Han, J., editors (2001). Geographic Data Mining and Knowledge Discovery. CRC Press.Google Scholar
  18. Okabe, A., Okunuki, K., and Shiode, S. (2006). Sanet: A toolbox for spatial analysis on a network. Geographical Analysis, 38(1):57–66.CrossRefGoogle Scholar
  19. O’Sullivan, D. and Unwin, D. (2002). Geographic Information Analysis. Wiley.Google Scholar
  20. Ratcliffe, J. H. (2004). The hotspot matrix: A framework for the spatio-temporal targeting of crime reduction. Police Practice and Research, 5:05–23.CrossRefGoogle Scholar
  21. Ratcliffe, J. H. and McCullagh, M. J. (1998). Aoristic crime analysis. International Journal of Geographical Information Science, 12:751–764.CrossRefGoogle Scholar
  22. Rich, T. (2001). Crime mapping and analysis by community organizations in hart-ford, connecticut. National Institute of Justice: Research in Brief, pages 1–11.Google Scholar
  23. Rote, G. (1997). Binary trees having a given number of nodes with 0, 1, and 2 children. S´eminaire Lotharingien de Combinatoire, B38b:6 pages.Google Scholar
  24. Spooner, P. G., Lunt, I. D., Okabe, A., and Shiode, S. (2004). Spatial analysis of roadside Acacia populations on a road network using the network k-function. Landscape Ecology, 19:491–499.CrossRefGoogle Scholar
  25. Steenberghen, T., Dufays, T., Thomas, I., and Flahaut, B. (2004). Intra-urban location and clustering of road accidents using GIS: a Belgian example. International Journal of Geographical Information Science, 18:169–181.CrossRefGoogle Scholar
  26. Stillwell, J. and Clarke, G. (2005). Applied GIS and Spatial Analysis. Wiley.Google Scholar
  27. Yamada, I. and Thill, J. (2007). Local indicators of network-constrained clusters in spatial point patterns. Geographical Analysis, 39:268–292.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Kevin Buchin
    • 1
    Email author
  • Sergio Cabello
    • 2
  • Joachim Gudmundsson
    • 3
  • Maarten Löffler
    • 1
  • Jun Luo
    • 4
  • Günther Rote
    • 5
  • Rodrigo I.Silveira
    • 1
  • Bettina Speckmann
    • 6
  • Thomas Wolle
    • 3
  1. 1.Department of Information and Computing SciencesUtrecht UniversityThe Netherlands
  2. 2.Department of MathematicsInst. for Math., Physics and MechanicsSlovenia
  3. 3.NICTASydneyAustralia
  4. 4.Shenzhen Institute of Advanced TechnologyChinese Academy of SciencesChina
  5. 5.Institut für InformatikFreie Universität BerlinGermany
  6. 6.Department of Mathematics and Computer ScienceTU EindhovenThe Netherlands

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