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Uncertainty in Spatial Trajectories

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Computing with Spatial Trajectories

Abstract

This chapter presents a systematic overview of the various issues and solutions related to the notion of uncertainty in the settings of moving objects trajectories. The sources of uncertainty in this context are plentiful: from the mere fact that the positioning devices are inherently imprecise, to the pragmatic aspect that, although the objects are moving continuously, location-based servers can only be updated in discrete times. Hence come the problems related to modelling and representing the uncertainty in Moving Objects Databases (MOD) and, as a consequence, problems of efficient algorithms for processing various spatio-temporal queries of interest. Given the ever-presence of uncertainty since the dawn of philosophy through modern day nano-level science, after a brief introduction, we present a historic overview of the role of uncertainty in parts of the evolution of the human thought in general, and Computer Science (CS) and databases in particular, which are relevant to this chapter. The focus of this chapter, however, will be on the impact that capturing the uncertainty in the syntax of the popular spatio-temporal queries has on their semantics and processing algorithms. We also consider the impact of different models in different settings – e.g., free motion; road-network constrained motion – and discuss the main issues related to exploiting such semantic dimension( s) for efficient query processing.

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References

  1. Abiteboul, S., Kanellakis, P.C., Grahne, G.: On the representation and querying of sets of possible worlds. In: SIGMOD Conference, pp. 34–48 (1987)

    Google Scholar 

  2. Aggarwal, C.C., Yu, P.S.: A survey of uncertain data algorithms and applications. IEEE Trans. Knowl. Data Eng. 21(5), 609–623 (2009)

    Article  Google Scholar 

  3. Alchourr´on, C., G¨ardenfors, P., Makinson, D.: On the logic of theory change. Journal of Symbolic Logic 50, 510–530 (1985)

    Google Scholar 

  4. Ali, M.E., Tanin, E., Zhang, R., Kotagiri, R.: Probabilistic voronoi diagrams for processing moving nearest neighbor queries (2011). (personal communication, manuscript under revision)

    Google Scholar 

  5. de Almeida, V.T., G¨uting, R.H.: Supporting uncertainty in moving objects in network databases. In: GIS, pp. 31–40 (2005)

    Google Scholar 

  6. Antova, L., Koch, C., Olteanu, D.: 10(106) worlds and beyond: efficient representation and processing of incomplete information. VLDB Journal 18(5), 1021–1040 (2009)

    Article  Google Scholar 

  7. Apt, K., Blair, H.: Arithmetic classification of perfect models of stratified programs. In: R. Kowalski, K. Bowen (eds.) Proc. 5th International Conference and Symposium on Logic Programming, pp. 765–779. Seattle, Washington (August 15–19, 1988)

    Google Scholar 

  8. Beckmann, N., Kriegel, H., Schneider, R., Seeger, B.: The r∗ tree: An efficient and robust access method for points and rectangles. In: ACM SIGMOD (1990)

    Google Scholar 

  9. Benetis, R., Jensen, C.S., Karciauskas, G., Saltenis, S.: Nearest and reverse nearest neighbor queries for moving objects. VLDB Journal 15(3), 229–249 (2006)

    Article  Google Scholar 

  10. Bernecker, T., Emrich, T., Kriegel, H.P., Mamoulis, N., Renz, M., Z¨u e, A.: A novel probabilistic pruning approach to speed up similarity queries in uncertain databases. In: ICDE, pp. 339–350 (2011)

    Google Scholar 

  11. Bernecker, T., Kriegel, H.P., Mamoulis, N., Renz, M., Z¨u e, A.: Scalable probabilistic similarity ranking in uncertain databases. IEEE Trans. Knowl. Data Eng. 22(9), 1234–1246 (2010)

    Google Scholar 

  12. Biazzo, V., Giugno, R., Lukasiewicz, T., Subrahmanian, V.S.: Temporal probabilistic object bases. IEEE Trans. Knowl. Data Eng. 15(4), 921–939 (2003)

    Article  Google Scholar 

  13. Buh, I.: Epistemic Logic in the Middle Ages. Routledge (1993) 14. Cai, Y., Hua, K., Cao, G.: Processing range-monitoring queries on heterogeneous mobile objects. In: International conference on Mobile Data Management (MDM) (2004)

    Google Scholar 

  14. Cao, H.,Wolfson, O., Trajcevski, G.: Spatio-temporal data reduction with deterministic error bounds. VLDB Journal 15(3) (2006)

    Google Scholar 

  15. Cavallo, R., Pittarelli, M.: The theory of probabilistic databases. In: VLDB, pp. 71–81 (1987)

    Google Scholar 

  16. Chellas, B.: Modal Logic: An Introduction. Cambridge University Press (1980)

    Google Scholar 

  17. Chen, J., Cheng, R., Mokbel, M.F., Chow, C.Y.: Scalable processing of snapshot and continuous nearest-neighbor queries over one-dimensional uncertain data. VLDB Journal 18(5), 1219–1240 (2009)

    Article  Google Scholar 

  18. Chen, T., Schneider, M.: Data structures and intersection algorithms for 3d spatial data types. In: GIS (2009)

    Google Scholar 

  19. Cheng, R., Chen, J., Mokbel, M.F., Chow, C.Y.: Probabilistic verifiers: Evaluating constrained nearest-neighbor queries over uncertain data. In: ICDE (2008)

    Google Scholar 

  20. Cheng, R., Kalashnikov, D.V., Prabhakar, S.: Querying imprecise data in moving objects environments. IEEE-Trans. Knowl. Data Eng. 16(9) (2004)

    Google Scholar 

  21. Cheng, R., Xie, X., Yiu, M.L., Chen, J., Sun, L.: Uv-diagram: A voronoi diagram for uncertain data. In: ICDE, pp. 796–807 (2010)

    Google Scholar 

  22. Chomicki, J.: Temporal query languages: A survey. In: ICTL, pp. 506–534 (1994)

    Google Scholar 

  23. Chon, H.D., Agrawal, D., Abbadi, A.E.: Range and knn query processing for moving objects in grid model. Mobile Networks and Applications 8 (2003)

    Google Scholar 

  24. Chow, C.Y., Mokbel, M.F., Liu, X.: Spatial cloaking for anonymous location-based services in mobile peer-to-peer environments. GeoInformatica 15(2), 351–380 (2011)

    Article  Google Scholar 

  25. Civilis, A., Jensen, C.S., Pakalnis, S.: Techniques for efficient road-network-based tracking of moving objects. IEEE Trans. Knowl. Data Eng. 17(5) (2005)

    Google Scholar 

  26. of Defense, U.S.D.: Navstar gps: Global positioning system standard (2008)

    Google Scholar 

  27. Demiryurek, U., Pan, B., Kashani, F.B., Shahabi, C.: Towards modeling the traffic data on road networks. In: GIS-IWCTS (2009)

    Google Scholar 

  28. Detlovs, V., Podnieks, K.: Introduction to Mathematical Logic. University of Latvia (2011). Hyper-textbook for students

    Google Scholar 

  29. Ding, Z.: Utr-tree: An index structure for the full uncertain trajectories of networkconstrained moving objects. In: MDM, pp. 33–40 (2008)

    Google Scholar 

  30. Ding, Z., G¨uting, R.H.: Uncertainty management for network constrained moving objects. In: DEXA, pp. 411–421 (2004)

    Google Scholar 

  31. Egenhofer, M., Franzosa, R.: Point set topological relations. International Journal of Geographical Information Systems 5 (1991)

    Google Scholar 

  32. Egenhofer, M.J., Dube, M.P.: Topological relations from metric refinements. In: GIS (2009)

    Google Scholar 

  33. Erwig, M., Schneider, M.: Spatio-temporal predicates. IEEE Trans. Knowl. Data Eng. 14(4), 881–901 (2002)

    Article  Google Scholar 

  34. Etzion, O., Jajodia, S., (eds.), S.S.: Temporal Databases: Research and Practice. Springer, LNCS (1998)

    Google Scholar 

  35. Fagin, R., Ullman, J., Vardi, M.: On the semantics of updates in databases. In: Proc. ACM PODS, pp. 352–365 (1983)

    Google Scholar 

  36. Gedik, B., Liu, L.: Mobieyes: A distributed location monitoring service using moving location queries. IEEE Transactions on Mobile Computing 5(10) (2006)

    Google Scholar 

  37. George, B., Kim, S., Shekhar, S.: Spatio-temporal network databases and routing algorithms: A summary of results. In: SSTD (2007)

    Google Scholar 

  38. Ghica, O., Trajcevski, G., Zhou, F., Tamassia, R., Scheuermann, P.: Selecting tracking principals with epoch-awareness. In: Proceedings of the 18th ACMSIGSPATIAL GIS Conference, pp. 222–231 (2010)

    Google Scholar 

  39. Ginsberg, M.L., Smith, D.E.: Reasoning about action i: A possible worlds approach. Artif. Intell. 35(2), 165–195 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  40. Goguen, J.: The logic of inexact concepts. Synthese 19, 325–373 (1969)

    MATH  Google Scholar 

  41. Goldblatt, R.: Mathematical modal logic: A history of its evolution (2006). Http://homepages.mcs.vuw.ac.nz/ rob/papers/modalhist.pdf

    Google Scholar 

  42. Goodchild, M.F., Zhang, J., Kyriakidis, P.C.: Discriminant models of uncertainty in nominal fields. T. GIS 13(1), 7–23 (2009)

    Article  Google Scholar 

  43. von Gottfried Wilhelm Leibniz, F.: Theodicy: Essays on the Goodness of God, the Freedom of Man, and the Origin of Evil. Open Court (1998)

    Google Scholar 

  44. Gowrisankar, N., Nittel, S.: Reducing uncertainty in location prediction of moving objects in road networks. In: GIScience (2002)

    Google Scholar 

  45. Grant, J., Horty, J., Lobo, J., Minker, J.: View updates in stratified disjunctive deductive databases. Journal of Automated Reasoning 11, 249–267 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  46. Gudmundsson, J., van Kreveld, M.J.: Computing longest duration ocks in trajectory data In: GIS (2006)

    Google Scholar 

  47. G¨uting, R.H.: Gral: An extensible relational database system for geometric applications. In: VLDB (1989)

    Google Scholar 

  48. G¨uting, R.H.: An introduction to spatial database systems. VLDB J. 3(4), 357–399 (1994)

    Google Scholar 

  49. G¨uting, R.H., de Almeida, V.T., Ding, Z.: Modeling and querying moving objects in networks. VLDB Journal 15(2) (2006)

    Google Scholar 

  50. G¨uting, R.H., Behr, T., D¨untgen, C.: Secondo: A platform for moving objects database research and for publishing and integrating research implementations. IEEE Data Eng. Bull. 33(2), 56–63 (2010)

    Google Scholar 

  51. G¨uting, R.H., B¨ohlen, M.H., Erwig, M., Jensen, C.S., Lorentzos, N., Nardeli, E., Schneider, M., Viqueira, J.R.R.: Spatio-temporal models and languages: An approach based on data types. In: Spatio-Temporal Databases – the Chorochronos Approach (2003)

    Google Scholar 

  52. G¨uting, R.H., B¨ohlen, M.H., Erwig, M., Jensen, C.S., Lorentzos, N., Schneider, M., Vazirgiannis, M.: A foundation for representing and queirying moving objects. ACM TODS (2000)

    Google Scholar 

  53. G¨uting, R.H., B¨ohlen, M.H., Erwig, M., Jensen, C.S., Lorentzos, N.A., Schneider, M., Vazirgiannis, M.: A foundation for representing and querying moving objects. ACM Trans. Database Syst. 25(1) (2000)

    Google Scholar 

  54. G¨uting, R.H., Schneider, M.: Realm-based spatial data types: The rose algebra. VLDB J. 4(2), 243–286 (1995)

    Google Scholar 

  55. G¨uting, R.H., Schneider, M.: Moving Objects Databases. Morgan Kaufmann (2005)

    Google Scholar 

  56. Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: SIGMOD Conference, pp. 47–57 (1984)

    Google Scholar 

  57. Haas, P.J., Suciu, D.: Special issue on uncertain and probabilistic databases. VLDB Journal 18(5), 987–988 (2009)

    Article  Google Scholar 

  58. Hadjielefteriou, M., Kollios, G., Bakalov, P., Tsotras, V.: Complex spatio-temporal pattern queries. In: VLDB (2005)

    Google Scholar 

  59. Hadjieleftheriou, M., Kollios, G., Tsotras, V.J., Gunopulos, D.: Efficient indexing of spatiotemporal objects. In: EDBT (2002)

    Google Scholar 

  60. H¨agerstrand, T.: What about people in regional science? Papers of the Regional Science Association 24, 7–21 (1970)

    Google Scholar 

  61. He, G., Hou, J.C.: Tracking targets with quality in wireless sensor networks. In: 13th IEEE International Conference on Network Protocols (ICNP) (2005)

    Google Scholar 

  62. Herrick, P.: The Many Worlds of Logic. Oxford University Press (1999)

    Google Scholar 

  63. Hintikka, J.: Knowledge and Belief: An Introduction to the Logic of the Two Notions. Cornell University Press (1962)

    Google Scholar 

  64. Hjaltason, G.R., Samet, H.: Distance browsing in spatial databases. ACM Trans. Database Syst. 24(2), 265–318 (1999)

    Article  Google Scholar 

  65. Hornsby, K., Egenhofer, M.J.: Modeling moving objects over multiple granularities. Ann. Math. Artif. Intell. 36(1–2), 177–194 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  66. Huang, Y.K., Chen, C.C., Lee, C.: Continuous k -nearest neighbor query for moving objects with uncertain velocity. GeoInformatica 13(1) (2009)

    Google Scholar 

  67. Huang, Y.K., Lee, C.: Efficient evaluation of continuous spatio-temporal queries on moving objects with uncertain velocity. GeoInformatica 14(2), 163–200 (2010)

    Article  Google Scholar 

  68. Ilarri, S., Mena, E., Illarramendi, A.: Location-dependent query processing: Where we are and where we are heading. ACM Comput. Surv. 42(3) (2010)

    Google Scholar 

  69. online issue, F.: (2006). Http://www.forbes.com/home/digitalentertainment/2006/ 04/13/google-aol-yahoo-cx rr 0417maps.html

    Google Scholar 

  70. Iwerks, G.S., Samet, H., Smith, K.P.: Maintenance of k-nn and spatial join queries on continuously moving points. ACM Trans. Database Syst. 31(2) (2006)

    Google Scholar 

  71. Jensen, C.S., Snodgrass, R.T.: Temporal data management. IEEE Trans. Knowl. Data Eng. 11(1), 36–44 (1999)

    Article  Google Scholar 

  72. Jeong, J., Guo, S., He, T., Du, D.: Apl: Autonomous passive localization for wireless sensors deployed in road networks. In: INFOCOM (2008)

    Google Scholar 

  73. Jeung, H., Liu, Q., Shen, H.T., Zhou, X.: A hybrid prediction model for moving objects. In: ICDE, pp. 70–79 (2008)

    Google Scholar 

  74. Jeung, H., Yiu, M.L., Zhou, X., Jensen, C.S., Shen, H.T.: Discovery of convoys in trajectory databases. PVLDB 1(1) (2008)

    Google Scholar 

  75. Kainz, W., Egenhofer, M., Greasley, I.: Modeling spatial relations and operations with partially ordered sets. International Journal of Geographical Information Systems 7(3) (1993)

    Google Scholar 

  76. Kanjilal, V., Liu, H., Schneider, M.: Plateau regions: An implementation concept for fuzzy regions in spatial databases and gis. In: IPMU, pp. 624–633 (2010)

    Google Scholar 

  77. Keogh, E.J.: A decade of progress in indexing and mining large time series databases. In: VLDB (2006) 79. Keogh, E.J., Chakrabarti, K., Mehrotra, S., Pazzani, M.J.: Locally adaptive dimensionality reduction for indexing large time series databases. In: SIGMOD Conference (2001)

    Google Scholar 

  78. Koubarakis, M., Sellis, T., Frank, A., Grumbach, S., G¨uting, R., Jensen, C., Lorentzos, N., Manolopoulos, Y., Nardelli, E., Pernici, B., Scheck, H.J., Scholl, M., Theodoulidis, B., Tryfona, N. (eds.): Spatio-Temporal Databases – the CHOROCHRONOS Approach. Springer-Verlag (2003)

    Google Scholar 

  79. Kripke, S.: Semantical considerations on modal logic. Acta Philosophica Fennica 16 (1963)

    Google Scholar 

  80. Kuijpers, B., Grimson, R., Othman, W.: An analytic solution to the alibi query in the spacetime prisms model for moving object data. International Journal of Geographical Information Science 25(2), 293–322 (2011)

    Article  Google Scholar 

  81. Kuijpers, B., Miller, H.J., Neutens, T., Othman, W.: Anchor uncertainty and space-time prisms on road networks. International Journal of Geographical Information Science 24(8), 1223–1248 (2010)

    Article  Google Scholar 

  82. Kuijpers, B., Moelans, B., Othman, W., Vaisman, A.A.: Analyzing trajectories using uncertainty and background information. In: SSTD, pp. 135–152 (2009)

    Google Scholar 

  83. Kuijpers, B., Othman, W.: Modelling uncertainty on road networks via space-time prisms. Int.l Journal on GIS 23(9) (2009)

    Google Scholar 

  84. Kuijpers, B., Othman, W.: Trajectory databases: data models, uncertainty and complete query languages. Journal of Computer and System Sciences (2009). Doi:10.1016/j.jcss.2009.10.002

    Google Scholar 

  85. Lange, R., Farrell, T., D¨urr, F., Rothermel, K.: Remote real-time trajectory simplification. In: PerCom (2009)

    Google Scholar 

  86. Lange, R., Weinschrott, H., Geiger, L., Blessing, A., D¨urr, F., Rothermel, K., Sch¨utze, H.: On a generic uncertainty model for position information. In: QuaCon, pp. 76–87 (2009)

    Google Scholar 

  87. Lee, D.L., Zhu, M., Hu, H.: When location-based services meet databases. Mobile Information Systems 1(2), 81–90 (2005)

    Google Scholar 

  88. Lema, J.A., Forlizzi, L., G¨uting, R.H., Nardelli, E., Schneider, M.: Algorithms for moving objects databases. Computing Journal 46(6) (2003)

    Google Scholar 

  89. Li, G., Li, Y., Shu, L., Fan, P.: Cknn query processing over moving objects with uncertain speeds in road networks. In: APWeb, pp. 65–76 (2011)

    Google Scholar 

  90. Lian, X., 0002, L.C.: Probabilistic ranked queries in uncertain databases. In: EDBT, pp. 511–522 (2008)

    Google Scholar 

  91. Lin, D., Cui, B., Yang, D.: Optimizing moving queries over moving object data streams. In: DASFAA, pp. 563–575 (2007)

    Google Scholar 

  92. Liu, H., Schneider, M.: Querying moving objects with uncertainty in spatio-temporal databases. In: DASFAA (1), pp. 357–371 (2011)

    Google Scholar 

  93. Lynch, J.D., Chen, X., Hui, R.B.: A multimedia approach to visualize and interact with large scale mobile lidar data. In: ACM Multimedia, pp. 1689–1692 (2010)

    Google Scholar 

  94. Ma, C.: Spatio-temporal variograms and covariance models. Advances in Applied Probability 37(3), 706–725 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  95. Mamoulis, N., Cao, H., Kollios, G., Hadjieleftheriou, M., Tao, Y., Cheung, D.W.: Mining, indexing, and querying historical spatiotemporal data. In: International Conference on Knowledge Discovery and Data Mining, pp. 236–245 (2004)

    Google Scholar 

  96. Minker, J., Lobo, J., Rajasekar, A.: Circumscription and disjunctive logic programming. In: V. Lifschitz (ed.) Artificial Intelligence and Mathematical Theory of Computation, pp. 281–304. Academic Press (1991)

    Google Scholar 

  97. Mokbel, M.F., Aref, W.G.: SOLE: Scalable on-line execution of continuous queries on spatio-temporal data streams. VLDB Journal 17(5), 971–985 (2008)

    Article  Google Scholar 

  98. Mokbel, M.F., Aref,W.G.: SOLE: scalable on-line execution of continuous queries on spatiotemporal data streams. VLDB Journal 17(5), 971–995 (2008)

    Article  Google Scholar 

  99. Mokbel, M.F., Chow, C.Y., Aref, W.G.: The new casper: Query processing for location services without compromising privacy. In: VLDB (2006)

    Google Scholar 

  100. Mokbel, M.F., Xing, X., Hammad, M., Aref, W.G.: Continuous query processing of spatiotemoral data streams in place. The GeoInformatica Journal 9(4) (2005)

    Google Scholar 

  101. Mokhtar, H., Su, J.: Questo: A query language for uncertain and exact spatio-temporal objects. In: ADBIS, pp. 184–198 (2008)

    Google Scholar 

  102. Mokhtar, H., Su, J., Ibarra, O.: On moving objects queries. In: PODS (2002)

    Google Scholar 

  103. Mouratidis, K., Yiu, M.L., Papadias, D., Mamoulis, N.: Continuous nearest neighbor monitoring in road networks. In: VLDB, pp. 43–54 (2006)

    Google Scholar 

  104. du Mouza, C., Rigaux, R.: Multi-scale classification of moving objects trajectories. In: SSDBM (2004)

    Google Scholar 

  105. O Rourke, J.: Computational Geometry in C. Cambridge University Press (2000)

    Google Scholar 

  106. Othman,W.: Uncertainty management in trajectory databases. Phd thesis, Hasselt University (Belgium) (2009)

    Google Scholar 

  107. Pasquale, A.D., Forlizzi, L., Jensen, C.S., Manolopoulos, Y., Nardelli, E., Pfoser, D., Proietti, G., Saltenis, S., Theodoridis, Y., Tzouramanis, T.: Access methods and query processing techniques. In: Spatio-Temporal Databases: the Chorochronos Approach (2003)

    Google Scholar 

  108. Pattem, S., Poduri, S., Krishnamachari, B.: Energy-quality tradeoffs for target tracking in wireless sensor networks. In: IPSN (2003)

    Google Scholar 

  109. Pei, J., Hua, M., Tao, Y., Lin, X.: Query answering techniques on uncertain and probabilistic data: tutorial summary. In: ACM SIGMOD (2008)

    Google Scholar 

  110. Pelanis, M., Saltenis, S., Jensen, C.S.: Indexing the past, present, and anticipated future positions of moving objects. ACM Trans. Database Syst. 31(1) (2006)

    Google Scholar 

  111. Pfoser, D., Jensen, C.S.: Capturing the uncertainty of moving objects representation. In: SSD (1999)

    Google Scholar 

  112. Pfoser, D., Tryfona, N.: Capturing fuzziness and uncertainty of spatiotemporal objects. In: ADBIS, pp. 112–126 (2001)

    Google Scholar 

  113. Pfoser, D., Tryfona, N., Jensen, C.S.: Indeterminacy and spatiotemporal data: Basic definitions and case study. GeoInformatica 9(3) (2005)

    Google Scholar 

  114. Popivanov, I., Miller, R.J.: Similarity search over time-series data using wavelets. In: ICDE (2002)

    Google Scholar 

  115. Prabhakar, S., Xia, Y., Khalashnikov, D., Aref, W., Hambrusch, S.: Query indexing and velocity constrained indexing: Scalable techniques for continuous queries on moving objects. IEEE - TRANS. KNOWL. DATA ENG. 51(10) (2002)

    Google Scholar 

  116. Qi, Y., Jain, R., Singh, S., Prabhakar, S.: Threshold query optimization for uncertain data. In: SIGMOD Conference, pp. 315–326 (2010)

    Google Scholar 

  117. Raptopoulou, K., Papadopoulos, A., Manolopoulos, Y.: Fast nearest-neighbor query processing in moving-object atabases. GeoInformatica 7(2), 113–137 (2003)

    Article  Google Scholar 

  118. Renz, M., Cheng, R., Kriegel, H.P., Z¨u e, A., Bernecker, T.: Similarity search and mining in uncertain databases (tutorial). PVLDB 3(2), 1653–1654 (2010)

    Google Scholar 

  119. Reynolds, A., Ioacono, G.L.: On the simulation of particle trajectories in turbulent ows. Physics of Fluids 16(12) (2004)

    Google Scholar 

  120. Rigaux, P., Scholl, M., Voisard, A.: Introduction to Spatial Databases: Applications to GIS. Morgan Kauffmann (2000)

    Google Scholar 

  121. Roberts, F.: Tolerance geometry. Notre Dame Journal of Formal Logic 14(1), 68–76 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  122. Roussopoulos, N., Kelley, S., Vincent, F.: Nearest neighbor queries. In: SIGMOD Conference, pp. 71–79 (1995)

    Google Scholar 

  123. Sarma, A.D., Benjelloun, O., Halevy, A.Y., Nabar, S.U., Widom, J.: Representing uncertain data: models, properties, and algorithms. VLDB Journal 18(5), 989–1019 (2009)

    Article  Google Scholar 

  124. Schiller, J., (editors), A.V.: Location-Based Services. Morgan Kaufmann (2004)

    Google Scholar 

  125. Schneider, M.: Uncertainty management for spatial data in databases: Fuzzy spatial data types. In: SSD, pp. 330–351 (1999)

    Google Scholar 

  126. Schneider, M.: Fuzzy spatial data types for spatial uncertainty management in databases. In: Handbook of Research on Fuzzy Information Processing in Databases, pp. 490–515 (2008)

    Google Scholar 

  127. Shahabi, C., Kolahdouzan, M.R., Sharifzadeh, M.: A road network embedding technique for k-nearest neighbor search in moving object databases. GeoInformatica 7(3), 255–273 (2003)

    Article  Google Scholar 

  128. Shekhar, S., Chawla, S.: Spatial Databases: A Tour. Prentice Hall (2003)

    Google Scholar 

  129. Sistla, A.P., Wolfson, O., Chamberlain, S., Dao, S.: Modeling and querying moving objects. In: 13th Int l Conf. on Data Engineering (ICDE) (1997)

    Google Scholar 

  130. Snodgrass, R.T., B¨ohlen, M.H., Jensen, C.S., Steiner, A.: Transitioning temporal support in tsql2 to sql3. In: Temporal Databases, Dagstuhl, pp. 150–194 (1997)

    Google Scholar 

  131. Soliman, M.A., Ilyas, I.F., Chang, K.C.C.: Top-k query processing in uncertain databases. In: ICDE (2007)

    Google Scholar 

  132. Suciu, D., Dalvi, N.N.: Foundations of probabilistic answers to queries. In: ACM SIGMOD (2005). Tutorial

    Google Scholar 

  133. Sundararaman, B., Buy, U., Kshemkalyani, A.D.: Clock synchronization for wireless sensor networks: a survey. Ad Hoc Networks 3(3), 281–323 (2005)

    Article  Google Scholar 

  134. Szewczyk, R., Mainwaring, A.M., Polastre, J., Anderson, J., Culler, D.E.: An analysis of a large scale habitat monitoring application. In: SenSys, pp. 214–226 (2004)

    Google Scholar 

  135. Tanin, E., Chen, S., Tatemura, J., Hsiung, W.P.: Monitoring moving objects using low frequency snapshots in sensor networks. In: MDM (2008)

    Google Scholar 

  136. Tao, Y., Faloutsos, C., Papadias, D., 0002, B.L.: Prediction and indexing of moving objects with unknown motion patterns. In: SIGMOD Conference, pp. 611–622 (2004)

    Google Scholar 

  137. Tao, Y., Papadias, D.: Spatial queries in dynamic environments. ACM Trans. Database Syst. 28(2) (2003)

    Google Scholar 

  138. Tao, Y., Papadias, D., Shen, Q.: Continuous nearest neighbor search. In: VLDB (2002)

    Google Scholar 

  139. Tao, Y., Papadias, D., Sun, J.: The tpr∗−tree: An optimized spatio-temporal access method for predictive queries. In: VLDB (2003)

    Google Scholar 

  140. Tao, Y., Xiao, X., Cheng, R.: Range search on multidimensional uncertain data. ACM Trans. Database Syst. 32(3), 15 (2007)

    Article  Google Scholar 

  141. Tøssebro, E., Nygard, M.: Uncertainty in spatiotemporal databases. In: ADVIS, pp. 43–53 (2002)

    Google Scholar 

  142. Trajcevski, G., Cao, H., Scheuermann, P., Wolfson, O., Vaccaro, D.: On-line data reduction and the quality of history in moving objects databases. In: MobiDE, pp. 19–26 (2006)

    Google Scholar 

  143. Trajcevski, G., Choudhary, A., Wolfson, O., Li, Y., Li, G.: Uncertain range queries for necklaces. In: MDM (2010)

    Google Scholar 

  144. Trajcevski, G., Ghica, O.C., Scheuermann, P.: Tracking-based trajectory data reduction in wireless sensor networks. In: SUTC/UMC, pp. 99–106 (2010)

    Google Scholar 

  145. Trajcevski, G., Tamassia, R., Cruz, I., Scheuermann, P., Hartglass, D., Zamierowski, C.: Ranking continuous nearest neighbors for uncertain trajectories. VLDB Journal (2011). (accepted, to appear)

    Google Scholar 

  146. Trajcevski, G., Tamassia, R., Ding, H., Scheuermann, P., Cruz, I.F.: Continuous probabilistic nearest-neighbor queries for uncertain trajectories. In: EDBT (2009)

    Google Scholar 

  147. Trajcevski, G.,Wolfson, O., Hinrichs, K., Chamberlain, S.: Managing uncertainty in moving objects databases. ACM Trans. Database Syst. 29(3) (2004)

    Google Scholar 

  148. Trajcevski, G., Wolfson, O., Zhang, F., Chamberlain, S.: The geometry of uncertainty in moving objects databases. In: International Conference on Extending Database Technology (EDBT) (2002)

    Google Scholar 

  149. Umer, M., Kulik, L., Tanin, E.: Spatial interpolation in wireless sensor networks: localized algorithms for variogram modeling and kriging. GeoInformatica 14(1), 101–134 (2010)

    Article  Google Scholar 

  150. UNISYS: 2009 hurrican/tropical data for atlantic. http://weather.unisys.com/hurricane/atlantic/2009/index.htm (2009)

  151. Vaisman, A.A., Zim´anyi, E.: What is spatio-temporal data warehousing? In: DaWaK, pp. 9–23 (2009)

    Google Scholar 

  152. Vazirgiannis, M., Wolfson, O.: A spatiotemporal model and language for moving objects on road networks. In: SSTD (2001)

    Google Scholar 

  153. Vlachos, M., Hadjielefteriou, M., Gunopulos, D., Keogh, E.: Indexing multidimensional time-series. VLDB Journal 15(1) (2006)

    Google Scholar 

  154. Weibel, R.: Generalization of spatial data: Principles and selected algorithms. In: Algorithmic Foundations of Geographic Information Systems. LNCS Springer Verlag (1996)

    Google Scholar 

  155. Wilke, G., Frank, A.F.: Tolerance geometry – euclid s first postulate for points and lines with extension. In: Proceedings of the 18th ACM SIGSPATIAL GIS Conference, pp. 162–171 (2010)

    Google Scholar 

  156. Winslett, M.: Reasoning about action using a possible model approach. In: Proc. of the Seventh National Conference on Artificial Intelligence, pp. 89–93 (1988)

    Google Scholar 

  157. Winter, S., Yin, Z.C.: Directed movements in probabilistic time geography. International Journal of Geographical Information Science 24(9) (2010)

    Google Scholar 

  158. Winter, S., Yin, Z.C.: The elements of probabilistic time geography. GeoInformatica 15(3), 417–434 (2011)

    Article  Google Scholar 

  159. Wolfson, O., Chamberlain, S., Dao, S., Jiang, L., Mendez, G.: Cost and imprecision in modeling the position of moving objects. In: 14 Int l Conf. on Data Engineering (ICDE) (1998)

    Google Scholar 

  160. Wolfson, O., Sistla, A.P., Chamberlain, S., Yesha, Y.: Updating and querying databases that track mobile units. Distributed and Parallel Databases 7 (1999)

    Google Scholar 

  161. Wolfson, O., Xu, B., Chamberlain, S., Jiang, L.: Moving objects databases: Issues and solutions. In: SSDB (1999)

    Google Scholar 

  162. Xing, X., Mokbel, M.F., Aref, W.G., Hambrusch, S.E., Prabhakar, S.: Scalable spatiotemporal continuous query processing for location-aware services. In: International Conference on Scientific and Statistical Database Management (SSDBM) (2004)

    Google Scholar 

  163. Xu, Y., Lee,W.C.: Compressing moving object trajectory in wireless sensor networks. IJDSN 3(2) (2007)

    Google Scholar 

  164. Yang, J., Hu, M.: Trajpattern: Mining sequential patterns from imprecise trajectories of mobile objects. In: International Conference on Extending Database Technology, pp. 664–681 (2006)

    Google Scholar 

  165. Yi, K., Li, F., Kollios, G., Srivastava, D.: Efficient processing of top-k queries in uncertain databases. In: ICDE, pp. 1406–1408 (2008)

    Google Scholar 

  166. Yiu, M.L., Mamoulis, N., Papadias, D.: Aggregate nearest neighbor queries in road networks. IEEE Trans. Knowl. Data Eng. 17(6) (2005)

    Google Scholar 

  167. Yoon, H., Shahabi, C.: Robust time-referenced segmentation of moving object trajectories. In: ICDM (2008)

    Google Scholar 

  168. Yu, B., Kim, S.H., Alkobaisi, S., Bae, W.D., Bailey, T.: The tornado model: Uncertainty model for continuously changing data. In: DASFAA, pp. 624–636 (2007)

    Google Scholar 

  169. Yu, X., Mehrotra, S.: Capturing uncertainty in spatial queries over imprecise data. In: DEXA, pp. 192–201 (2003)

    Google Scholar 

  170. Yu, X., Pu, K.Q., Koudas, N.: Monitoring k-nearest neighbor queries over moving objects. In: ICDE, pp. 631–642 (2005)

    Google Scholar 

  171. Zadeh, L.A.: Commonsense knowledge representation based on fuzzy logic. IEEE Computer 16(10), 61–65 (1983)

    Google Scholar 

  172. Zadeh, L.A.: Granular computing - computing with uncertain, imprecise and partially true data. In: Int.l Symp. on Spatial Data Quality (2007)

    Google Scholar 

  173. Zhang, Q., Sobelman, G.E., He, T.: Gradient-based target localization in robotic sensor networks. Pervasive and Mobile Computing 5(1) (2009)

    Google Scholar 

  174. Zhang, Y., Cheng, R., Chen, J.: Evaluating continuous probabilistic queries over imprecise sensor data. In: DASFAA (1), pp. 535–549 (2010)

    Google Scholar 

  175. Zhao, Y., Aggarwal, C.C., Yu, P.S.: On wavelet decomposition of uncertain time series data sets. In: CIKM, pp. 129–138 (2010)

    Google Scholar 

  176. Zheng, K., Trajcevski, G., Zhou, X., Scheuermann, P.: Probabilistic range queries for uncertain trajectories on road networks. In: EDBT, pp. 283–294 (2011)

    Google Scholar 

  177. Zhong, Z., Zhu, T., Wang, D., He, T.: Tracking with unreliable node sequences. In: INFOCOM, pp. 1215–1223 (2009)

    Google Scholar 

  178. Zhu, X., Sarkar, R., Gao, J., Mitchell, J.S.B.: Light-weight contour tracking in wireless sensor networks. In: INFOCOM, pp. 1175–1183 (2008)

    Google Scholar 

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  1. Dept. of EECS, Northwestern University, 2145 Sheridan Rd., Evanston, Il, 60208, USA

    Goce Trajcevski

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    Yu Zheng

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    Xiaofang Zhou

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Trajcevski, G. (2011). Uncertainty in Spatial Trajectories. In: Zheng, Y., Zhou, X. (eds) Computing with Spatial Trajectories. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1629-6_3

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