Detecting Hotspots in Geographic Networks
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.
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- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Fotheringham, S. and Rogerson, P. (1994). Spatial Analysis and GIS. Taylor and Francis, London.Google Scholar
- Illinois Criminal Justice Information Authority (1996). STAC user manual.Google Scholar
- Kloks, T. (1993). Treewidth. PhD thesis, Utrecht University.Google Scholar
- Miller, H. and Han, J., editors (2001). Geographic Data Mining and Knowledge Discovery. CRC Press.Google Scholar
- O’Sullivan, D. and Unwin, D. (2002). Geographic Information Analysis. Wiley.Google Scholar
- 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
- 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
- Stillwell, J. and Clarke, G. (2005). Applied GIS and Spatial Analysis. Wiley.Google Scholar