Abstract
We outline our work on using bintrees as an efficient representation for qualitative information about spatial objects. Our approach represents each spatial object as a bintree satisfying the exact same qualitative relationships to other bintree representations as the corresponding spatial objects. We prove that such correct bintrees always exist and that they can be constructed as a sum of local representations, allowing a practically efficient construction. Our representation is both efficient, with respect to storage space and query time, and can represent many well-known qualitative relations, such as the relations in the Region Connection Calculus and Allen’s Interval Algebra.
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Notes
Note that deletion is trivial: We can delete any bintree representation without affecting the correctness of the remaining representations.
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References
PostGIS FAQ (2016) http://postgis.net/docs/PostGIS_FAQ.html. [Online; accessed 08.11.2016]
Allen JF (1983) Maintaining knowledge about temporal intervals. Commun ACM 26(11):832–843
Attene M, Campen M, Kobbelt L (2013) Polygon mesh repairing: an application perspective. ACM Comput Surv (CSUR) 45(2):15
Cohn AG, Bennett B, Gooday J, Gotts NM (1997) Qualitative spatial representation and reasoning with the region connection calculus. In: GeoInformatica, number 3 in 1. Springer, pp 275–316
Cohn AG, Gotts NM (1996) The ‘egg-yolk’ representation of regions with indeterminate boundaries. In: Burrough PA, Frank AU (eds) Geographic objects with indeterminate boundaries, vol 2. Taylor & Francis, London, pp 171–187
Guttman A (1984) R-trees: a dynamic index structure for spatial searching. In: Proceedings of the 1984 ACM SIGMOD International Conference on Management of data, SIGMOD ’84. ACM, New York, pp 47–57
Jin R, Wang G (2013) Simple, fast, and scalable reachability oracle. In: Proceedings of the VLDB endowment, number 14 in 6. VLDB Endowment, pp 1978–1989
Karlsen LH, Giese M (2015) A framework for constructing correct qualitative representations of geometries using mereology over bintrees. Ann Comput Sci Inf Syst 7:21–33
Karlsen LH, Giese M (2017) An efficient representation of qualitative spatial information using bintrees. Technical report, Department of Informatics, University of Oslo. http://hdl.handle.net/10852/53792
Karlsen LH, Giese M Qualitatively correct bintrees with roles. Technical Report 467, Department of Informatics, University of Oslo, 2017. (Submitted to COSIT’17)
Karp RM (1972) Reducibility among combinatorial problems. In: Complexity of computer computations. Springer, pp 85–103
Koubarakis M (2003) Spatio-temporal databases: The CHOROCHRONOS approach. Springer Science & Business Media, vol 2520
Kyzirakos K, Karpathiotakis M, Koubarakis M (2012) Strabon: a semantic geospatial dbms. In: ISWC’12. Springer, pp 295–311
Li S, Long Z, Liu W, Duckham M, Both A (2015) On redundant topological constraints. In: Artificial intelligence. Elsevier, vol 225, pp 51–76
Ligozat GÉ (1998) Reasoning about cardinal directions. In: Journal of Visual Languages & Computing, number 1 in 9. Elsevier, pp 23–44
Long Z (2017) Qualitative spatial and temporal representation and reasoning: efficiency in time and space. PhD thesis, University of Technology Sydney
Long Z, Duckham M, Li S, Schockaert S (2016) Indexing large geographic datasets with compact qualitative representation. In: International Journal of Geographical Information Science, number 6 in 30. Taylor & Francis, pp 1072–1094
Long Z, Schockaert S, Li S (2016) Encoding large RCC8 scenarios using rectangular pseudo-solutions. In: Proceedings, Fifteenth international conference on principles of knowledge representation and reasoning (KR 2016). AAAI Press, pp 463–472
Manolopoulos Y, Nanopoulos A, Papadopoulos AN, Theodoridis Y (2010) R-trees: theory and applications. Springer Science & Business Media, Berlin
Nguyen T (2009) Indexing PostGIS databases and spatial query performance evaluations. In: International Journal of Geoinformatics, number 3 in 5. Association for Geoinformation Technology
Nicholson P (2013) Space-efficient Data Structures in the word-RAM and Bitprobe Models. PhD thesis, University of Waterloo
Obe RO, Hsu LS (2015) PostGIS in Action, 2nd edn. Manning Publications Co., Greenwich
Papadias D, Sellis T (1993) The semantics of relations in 2D space using representative points: Spatial indexes. In: International conference on spatial information theory (COSIT 1993). Springer, pp 234– 247
Randell DA, Cui Z, Cohn AG (1992) A spatial logic based on regions and connection. In: Proceedings, Third international conference on principles of knowledge representation and reasoning (KR 1992). Morgan Kaufmann Publishers, pp 165–176
Renz J, Nebel B (1999) On the complexity of qualitative spatial reasoning: A maximal tractable fragment of the region connection calculus. In: Artificial Intelligence, number 1 in 108. Elsevier, pp 69–123
Samet H (2006) Object-based and image-based image representations. In: Foundations of multidimensional and metric data structures. Morgan-Kaufmann, San Francisco, pp 211–220
Samet H, Tamminen M (1985) Bintrees, csg trees, and time. In: Proceedings of the 12th Annual Conference on Computer Graphics and Interactive techniques, SIGGRAPH ’85. ACM, New York, pp 121–130
Sioutis M (2014) Triangulation versus graph partitioning for tackling large real world qualitative spatial networks. In: 2014 IEEE 26th International conference on tools with artificial intelligence (ICTAI). IEEE, pp 194–201
Sioutis M, Condotta J-F (2014) Tackling large qualitative spatial networks of scale-free-like structure. In: SETN. Springer, pp 178–191
Sioutis M, Long Z, Li S (2016) Efficiently reasoning about qualitative constraints through variable elimination. In: Proceedings of the 9th Hellenic conference on artificial intelligence. ACM
van Schaik SJ, de Moor O (2011) A memory efficient reachability data structure through bit vector compression. In: Proceedings of SIGMOD. ACM, pp 913–924
Vassilakopoulos M, Manolopoulos Y (2000) External balanced regular (x-BR) trees: new structures for very large spatial databases. In: Proceedings of the 8th International conference on human-computer interaction (HCI International ’99). Lawrence Erlbaum, pp 324–333
Wolter D, Kreutzmann A (2015) Analogical representation of RCC-8 for neighborhood-based qualitative spatial reasoning. In: Joint German/Austrian conference on artificial intelligence (Künstliche Intelligenz). Springer, pp 194–207
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Karlsen, L.H., Giese, M. Qualitatively correct bintrees: an efficient representation of qualitative spatial information. Geoinformatica 23, 689–731 (2019). https://doi.org/10.1007/s10707-019-00348-z
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DOI: https://doi.org/10.1007/s10707-019-00348-z