Skip to main content
Springer Nature Link
Log in

Distance-Constrained k Spatial Sub-Networks: A Summary of Results

  • Conference paper
  • First Online:
Geographic Information Science (GIScience 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9927))

Included in the following conference series:

Abstract

Given a graph and a set of spatial events, the goal of Distance-Constrained k Spatial Sub-Networks (DCSSN) problem is to find k sub-networks that meet a distance constraint and maximize the number of spatial events covered by the sub-networks. The DCSSN problem is important for many societal applications, such as police patrol assignment and emergency response assignment. The problem is NP-hard; it is computationally challenging because of the large size of the transportation network and the distance constraint. This paper proposes a novel approach for finding k sub-networks that maximize the coverage of spatial events under the distance constraint. Experiments and a case study using Chicago crime datasets demonstrate that the proposed algorithm outperforms baseline approaches and reduces the computational cost to create a DCSSN.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Agarwal, P.K., Procopiuc, C.M.: Exact and approximation algorithms for clustering. Algorithmica 33(2), 201–226 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aggarwal, C.C., et al.: Data Clustering: Algorithms and Applications. CRC Press, Boca Raton (2013)

    Google Scholar 

  3. Ahuja, R., Magnanti, T., Orlin, J., Weihe, K.: Network Flows: Theory, Algorithms and Applications. Prentice-Hall, Englewood Cliffs (1993)

    MATH  Google Scholar 

  4. Barthélemy, M.: Spatial networks. Phys. Rep. 499(1), 1–101 (2011)

    Article  MathSciNet  Google Scholar 

  5. Black, W.R., Thomas, I.: Accidents on Belgium’s motorways: a network autocorrelation analysis. J. Transp. Geogr. 6(1), 23–31 (1998)

    Article  Google Scholar 

  6. Buchin, K., et al.: Detecting hotspots in geographic networks. In: Sester, M., Bernard, L., Paelke, V. (eds.) Advances in GIScience. LNGC, pp. 217–231. Springer, Berlin (2009)

    Chapter  Google Scholar 

  7. Carmi, P., Katz, M.J., Lev-Tov, N.: Covering points by unit disks of fixed location. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 644–655. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Chazelle, B.M., et al.: On a circle placement problem. Computing 36(1–2), 1–16 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chen, Z., et al.: Discovering popular routes from trajectories. In: 2011 IEEE 27th International Conference on Data Engineering, pp. 900–911. IEEE (2011)

    Google Scholar 

  10. Chun, Y.: Modeling network autocorrelation within migration flows by eigenvector spatial filtering. J. Geogr. Syst. 10(4), 317–344 (2008)

    Article  Google Scholar 

  11. City of Chicago Data Potal, Crimes - 2001 to Present. https://data.cityofchicago.org/Public-Safety/Crimes-2001-to-present/ijzp-q8t2. Accessed Dec 2015

  12. Current, J., Pirkul, H., Rolland, E.: Efficient algorithms for solving the shortest covering path problem. Transp. Sci. 28(4), 317–327 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  13. Current, J., et al.: The shortest covering path problem-an application of locational constraints to network design. J. Reg. Sci. 24(2), 161–183 (1984)

    Article  Google Scholar 

  14. Current, J.R., Schilling, D.A.: The median tour and maximal covering tour problems: formulations and heuristics. Eur. J. Oper. Res. 73(1), 114–126 (1994)

    Article  MATH  Google Scholar 

  15. Current, J.R., Velle, C.R., Cohon, J.L.: The maximum covering/shortest path problem: a multiobjective network design and routing formulation. Eur. J. Oper. Res. 21(2), 189–199 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  16. Downs, J., Horner, M.: Network-based kernel density estimation for home range analysis. In: Proceedings of 9th International Conference on Geocomputation, Maynooth, Ireland (2007)

    Google Scholar 

  17. Ester, M., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: KDD, vol. 96, pp. 226–231 (1996)

    Google Scholar 

  18. Fotakis, D., et al.: Space efficient hash tables with worst case constant access time. Theor. Comput. Syst. 38(2), 229–248 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gandhi, R., Khuller, S., Srinivasan, A.: Approximation algorithms for partial covering problems. J. Algorithms 53(1), 55–84 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Ghasemalizadeh, H., Razzazi, M.: An improved approximation algorithm for the most points covering problem. Theor. Comput. Syst. 50(3), 545–558 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gonzalez, T.F.: Clustering to minimize the maximum intercluster distance. Theoret. Comput. Sci. 38, 293–306 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  22. Han, J., et al.: Data Mining: Concepts and Techniques. Elsevier, Amsterdam (2011)

    Google Scholar 

  23. Hifi, M., M’hallah, R.: A literature review on circle and sphere packing problems: models and methodologies. Adv. Oper. Res. (2009)

    Google Scholar 

  24. Hochbaum, D.S., Shmoys, D.B.: A best possible heuristic for the k-center problem. Math. Oper. Res. 10(2), 180–184 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  25. Hochbaum, D.S., Shmoys, D.B.: A unified approach to approximation algorithms for bottleneck problems. J. ACM (JACM) 33(3), 533–550 (1986)

    Article  MathSciNet  Google Scholar 

  26. LAPD Crime and Collision Raw Data for 2015. https://data.lacity.org/A-Safe-City/LAPD-Crime-and-Collision-Raw-Data-for-2015/ttiz-7an8. Accessed Dec 2015

  27. Li, X., Han, J., Lee, J.-G., Gonzalez, H.: Traffic density-based discovery of hot routes in road networks. In: Papadias, D., Zhang, D., Kollios, G. (eds.) SSTD 2007. LNCS, vol. 4605, pp. 441–459. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  28. Marchette, D.: Scan statistics on graphs. Wiley Interdiscip. Rev.: Comput. Stat. 4(5), 466–473 (2012)

    Article  Google Scholar 

  29. Murawski, L., Church, R.L.: Improving accessibility to rural health services: the maximal covering network improvement problem. Soc.-Econ. Plan. Sci. 43(2), 102–110 (2009)

    Article  Google Scholar 

  30. Okabe, A., Sugihara, K.: Spatial Analysis Along Networks: Statistical and Computational Methods. Wiley, Hoboken (2012)

    Book  MATH  Google Scholar 

  31. Okabe, A., Yamada, I.: The k-function method on a network and its computational implementation. Geogr. Anal. 33(3), 271–290 (2001)

    Article  Google Scholar 

  32. Oliver, D., et al.: A k-main routes approach to spatial network activity summarization. IEEE Trans. Knowl. Data Eng. 26(6), 1464–1478 (2014)

    Article  Google Scholar 

  33. OpenStreetMap. http://www.openstreetmap.org/. Accessed Sept 2015

  34. O’Sullivan, D., et al.: Geographic Information Analysis. Wiley, Hoboken (2014)

    Google Scholar 

  35. Priebe, C.E., et al.: Scan statistics on enron graphs. Comput. Math. Organ. Theor. 11(3), 229–247 (2005)

    Article  MATH  Google Scholar 

  36. Samet, H.: Foundations of Multidimensional and Metric Data Structures. Morgan Kaufmann, San Francisco (2006)

    MATH  Google Scholar 

  37. Shekhar, S., Chawla, S.: Spatial Databases: A Tour. Prentice Hall, Upper Saddle River (2003)

    Google Scholar 

  38. Shiode, S., Shiode, N.: Detection of multi-scale clusters in network space. Int. J. Geogr. Inf. Sci. 23(1), 75–92 (2009)

    Article  Google Scholar 

  39. Sørensen, T.: A method of establishing groups of equal amplitude in plant sociology based on similarity of species content and its application to analyses of the vegetation on danish commons. Biologiske Skrifter 5, 1–34 (1948)

    Google Scholar 

  40. Spooner, P.G., et al.: Spatial analysis of roadside acacia populations on a road network using the network k-function. Landsc. Ecol. 19(5), 491–499 (2004)

    Article  Google Scholar 

  41. Tan, P., et al.: Introduction to Data Mining. Addison-Wesley, Boston (2005)

    Google Scholar 

  42. Yamada, I., Thill, J.C.: Local indicators of network-constrained clusters in spatial point patterns. Geogr. Anal. 39(3), 268–292 (2007)

    Article  Google Scholar 

  43. Yang, K., et al.: Capacity-constrained network-Voronoi diagram. IEEE Trans. Knowl. Data Eng. 27(11), 2919–2932 (2015)

    Article  Google Scholar 

Download references

Acknowledgments

We would like to thank FAU under start-up funds for student support, equipment and travel.

Author information

Authors and Affiliations

  1. Florida Atlantic University, Boca Raton, USA

    KwangSoo Yang

Authors
  1. KwangSoo Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to KwangSoo Yang .

Editor information

Editors and Affiliations

  1. University of Texas at Austin , Austin, Texas, USA

    Jennifer A. Miller

  2. University of California at Berkeley , Berkeley, California, USA

    David O'Sullivan

  3. University of Wisconsin-Madison , Madison, Wisconsin, USA

    Nancy Wiegand

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Yang, K. (2016). Distance-Constrained k Spatial Sub-Networks: A Summary of Results. In: Miller, J., O'Sullivan, D., Wiegand, N. (eds) Geographic Information Science. GIScience 2016. Lecture Notes in Computer Science(), vol 9927. Springer, Cham. https://doi.org/10.1007/978-3-319-45738-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45738-3_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45737-6

  • Online ISBN: 978-3-319-45738-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics