Abstract
Given a set \(\mathcal O\) of observations, in the previous chapter, we developed a set of methods to find sets \(\mathcal E\) of explanations. However, these explanations consisted of points. When the geospatial resolution of the space\(\mathcal S\) is small, the non-determinism in our point-based geospatial abduction algorithms is negligible—making many points more or less “equivalent” as far as being potential partner locations. As such, users might want to get regions back as output to their geospatial abduction queries. Moreover, users might want to reason about real-valued points rather than points that are integer-valued. In this chapter, we develop the theory and algorithms required for reasoning in the real-valued domain with regions being returned to the user rather than points.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Alpaydin, E.: 2010. Introduction to Machine Learning. MIT Press, 2 edition, 2010.
Brantingham, P., Brantingham, P.: 2008. Crime Pattern Theory. In Enviromental Criminology and Crime Analysis, R. Wortley and L. Mazerolle, Eds., pages 78–93.
, Bylander, T., Allemang, D., Tanner, M., Josephson, J.R.: 1991. The Computational Complexity of Abduction, Arti cial Intelligence.
Liao, C., Hu, S.: 2009. Polynomial time approximation schemes for minimum disk cover problems, Journal of Combinatorial Optimization.
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: 2001. Introduction to Algorithms. MIT Press, second edition, 2001.
Eiter, T., Gottlob, G.: 1995. The complexity of logic-based abduction, J. ACM, 42, 1, pages 3–42.
Feige, U.: 1998. A threshold of ln n for approximating set cover, J. ACM, 45, 4, pages 634– 652.
Franceschetti, M., Cook, M., Bruck, J.: 2004. A Geometric Theorem for Network Design, IEEE Transactions on Computers, 53, 4, pages 483–489.
Fu, B, Chen, Z., Abdelguer, M.: 2007. An Almost Linear Time 2.8334-Approximation Algorithm for the Disc Covering Problem, AAIM 07: Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management, pages 317–326, Springer-Verlag.
Hochbaum,D.S.,Maass, W.: 1985. Approximation schemes for covering and packing problems in image processing and VLSI, J. ACM, 32, pages 130–136.
Megiddo, N., Supowit,K.J.: 1984. On the Complexity of Some Common Geometric Location Problems, SIAM Journal of Computing, 13, 1, pages 182–196.
, Nemhauser, G. L., Wolsey, L. A., Fisher, M.L.: 1978. An analysis of approximations for maximizing submodular set functions I, Mathematical Programming, 14, 1, pages 265–294.
Fredman, M.L., Tarjan, R.E.: 1987. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34(3):596–615, July 1987.
Freedman, D., Purves, R., Pisani, R.: 2007. Statistics. W.W. Norton and Co., 4 edition.
Garey, M.R., Johnson, D.S.: 1979. Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York, NY, USA.
Hochbaum, D.S.: 1982. Approximation Algorithms for the Set Covering and Vertex Cover Problems. SIAM Journal on Computing, 11(3):555–556.
Hochbaum, D.S.: 1997. Approximation Algorithms for NP-Complete Problems. PWS Publishing Co., 1997.
Hochbaum, D.S., Maass, W.: 1985 Approximation schemes for covering and packing problems in image processing and vlsi. Journal of the ACM, 32:130–136.
Jia, L., Rajaraman, R. Suel, T.: 2002. An ef cient distributed algorithm for constructing small dominating sets. Distrib. Comput., 15(4):193–205.
Johnson, D.S.: 1982. The np-completeness column: An ongoing guide. Journal of Algorithms, 3(2):182–195, 1982.
Karp, R.: 1972. Reducibility Among Combinatorial Problems. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, page 85–103.
Kuhn, F., Wattenhofer, R.: 2003. Constant-time distributed dominating set approximation. In In Proc. of the 22 nd ACM Symposium on the Principles of Distributed Computing (PODC, pages 25–32.
Lu, J., Nerode, A., Subrahmanian, V.S.: 1996. Hybrid Knowledge Bases, IEEE Transactions on Knowledge and Data Engineering, 8, 5, pages 773–785.
Lund, C., Yannakakis, M.: 1994. On the hardness of approximating minimization problems. Journal of the ACM, 41(5):960–981.
Papadimitriou, C.H.: 1981. Worst-Case and Probabilistic Analysis of a Geometric Location Problem, SIAM J. Comput., 10(3):542–557.
Paschos, V.T.: 1997. A survey of approximately optimal solutions to some covering and packing problems. ACM Comput. Surv., 29(2):171–209.
Reggia, J.A., Peng, Y.: 1990. Abductive inference models for diagnostic problem-solving. Springer-Verlag New York, Inc., New York, NY, USA.
Rimoin, A. et al.: Endemic Human Monkeypox, Democratic Republic of Congo, 2001–2004, Emerging Infectious Diseases, 13, 6, pages 934–937, 2007.
Rossmo, D. K., Rombouts, S.: 2008. Geographic Pro ling. In Enviromental Criminology and Crime Analysis, R. Wortley and L. Mazerolle, Eds. pages 136–149.
H. Samet.: The Design and Analysis of Spatial Data Structures, Addison Wesley, 1989.
Shakarian, P., Subrahmanian, V.S., Sapino, M.L. SCARE: A Case Study with Baghdad, Proc. 2009 Intl. Conf. on Computational Cultural Dynamics (eds. D. Nau, A. Mannes), Dec. 2009, AAAI Press.
Shakarian, P., Subrahmanian, V.S., Sapino, M.L. 2012. GAPS: Geospatial Abduction Problems, ACM Transactions on Intelligent Systems and Technology (TIST), 3, 1, to appear.
Shakarian, P., Subrahmanian, V.S. Region-based Geospatial Abduction with Counter-IED Applications, accepted for publication in:Wiil, U.K. (ed.).Counterterrorism and Open Source Intelligence, Springer Verlag Lecture Notes on Social Networks, to appear, 2011.
Shakarian, P., Nagel, M., Schuetzle, B., Subrahmanian, V.S. 2011. Abductive Inference for Combat: Using SCARE-S2 to Find High-Value Targets in Afghanistan, in Proc. 2011 Intl. Conf. on Innovative Applications of Arti cial Intelligence, Aug. 2011, AAAI Press.
Shakarian, P., Dickerson, J., Subrahmanian, V.S. 2012. Adversarial Geospatial Abduction Problems, ACM Transactions on Intelligent Systems and Technology (TIST), to appear.
Singh, M., Joshi, P.K., Kumar,M., Dash, P.P., Joshi, B.D.: Development of tiger habitat suitability model using geospatial tools: a case study in Achankmar Wildlife Sanctuary (AMWLS), Chhattisgarh India, Env. Monitoring and Assessment journal, Vol. 155, pages 555–567, 2009.
US Army: Intelligence Preparation of the Battle led (US Army Field Manual), FM 34–130 edition, 1994.
”Map of Special Groups Activity in Iraq, Institute for the Study of War”, Institute for the Study of War, 2008.
Vazirani, V.V.: 2004. Approximation Algorithms. Springer, March 2004.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Shakarian, P., Subrahmanian, V.S. (2011). Region-Based Geospatial Abduction. In: Geospatial Abduction. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1794-1_3
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1794-1_3
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-1793-4
Online ISBN: 978-1-4614-1794-1
eBook Packages: Computer ScienceComputer Science (R0)