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Studying the use and effect of graph decomposition in qualitative spatial and temporal reasoning

Published online by Cambridge University Press:  12 October 2016

Michael Sioutis ,
Yakoub Salhi  and
Jean-François Condotta
Michael Sioutis
Affiliation:
Université Lille-Nord de France, Artois, CRIL-CNRS UMR 8188, Rue Jean Souvraz – SP 18, F 62307 Lens, France e-mail: fsioutis@cril.fr, salhi@cril.fr, condottag@cril.fr
Yakoub Salhi
Affiliation:
Université Lille-Nord de France, Artois, CRIL-CNRS UMR 8188, Rue Jean Souvraz – SP 18, F 62307 Lens, France e-mail: fsioutis@cril.fr, salhi@cril.fr, condottag@cril.fr
Jean-François Condotta
Affiliation:
Université Lille-Nord de France, Artois, CRIL-CNRS UMR 8188, Rue Jean Souvraz – SP 18, F 62307 Lens, France e-mail: fsioutis@cril.fr, salhi@cril.fr, condottag@cril.fr
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Abstract

We survey the use and effect of decomposition-based techniques in qualitative spatial and temporal constraint-based reasoning, and clarify the notions of a tree decomposition, a chordal graph, and a partitioning graph, and their implication with a particular constraint property that has been extensively used in the literature, namely, patchwork. As a consequence, we prove that a recently proposed decomposition-based approach that was presented in the study by Nikolaou and Koubarakis for checking the satisfiability of qualitative spatial constraint networks lacks soundness. Therefore, the approach becomes quite controversial as it does not seem to offer any technical advance at all, while results of an experimental evaluation of it in a following work presented in the study by Sioutis become questionable. Finally, we present a particular tree decomposition that is based on the biconnected components of the constraint graph of a given large network, and show that it allows for cost-free utilization of parallelism for a qualitative constraint language that has patchwork for satisfiable atomic networks.

Type
Articles
Information
The Knowledge Engineering Review , Volume 32 , 2017 , e4
Copyright
© Cambridge University Press, 2017 

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References

Allen, J. F. 1981. An interval-based representation of temporal knowledge. In IJCAI.Google Scholar
Amaneddine, N., Condotta, J.-F. & Sioutis, M. 2013. Efficient approach to solve the minimal labeling problem of temporal and spatial qualitative constraints. In IJCAI.Google Scholar
Baget, J.-F. & Tognetti, Y. S. 2001. Backtracking through biconnected components of a constraint graph. In IJCAI.Google Scholar
Balbiani, P., Condotta, J.-F. & Cerro, L. F. d. 2002. Tractability results in the block algebra. Journal of Logic and Computation 12, 885–909.Google Scholar
Barabasi, A.-L. & Bonabeau, E. 2003. Scale-free networks. Scientific American 288, 50–59.Google Scholar
Beek, P. v. & Manchak, D. W. 1996. The design and experimental analysis of algorithms for temporal reasoning. Journal of Artificial Intelligence Research 4, 1–18.Google Scholar
Bhatt, M., Guesgen, H., Wölfl, S. & Hazarika, S. 2011. Qualitative spatial and temporal reasoning: emerging applications, trends, and directions. Spatial Cognition & Computation 11, 1–14.Google Scholar
Bliek, C. & Sam-Haroud, D. 1999. Path consistency on triangulated constraint graphs. In IJCAI.Google Scholar
Bodirsky, M. & Wölfl, S. 2011. RCC8 is polynomial on networks of bounded treewidth. In IJCAI.Google Scholar
Brand, S. 2004. Relation variables in qualitative spatial reasoning. In KI.Google Scholar
Chmeiss, A. & Condotta, J.-F. 2011. Consistency of triangulated temporal qualitative constraint networks. In ICTAI.Google Scholar
Condotta, J.-F. & D’Almeida, D. 2011. Consistency of qualitative constraint networks from tree decompositions. In TIME.Google Scholar
Condotta, J.-F., Dalmeida, D., Lecoutre, C. & Sais, L. 2006. From qualitative to discrete constraint networks. In KI Workshop on Qualitative Constraint Calculi.Google Scholar
Dechter, R. 2003. Constraint Processing. Elsevier Morgan Kaufmann.Google Scholar
Dechter, R. & Pearl, J. 1989. Tree clustering for constraint networks. Artificial Intelligence 38, 353–366.Google Scholar
Del Genio, C. I., Gross, T. & Bassler, K. E. 2011. All scale-free networks are sparse. Physical Review Letters 107, 178701.Google Scholar
Diestel, R. 2012. Graph Theory, 4th Edition, 173. Springer.Google Scholar
Duckham, M., Li, S., Liu, W. & Long, Z. 2014. On redundant topological constraints. In KR.Google Scholar
Dylla, F., Mossakowski, T., Schneider, T. & Wolter, D. 2013. Algebraic properties of qualitative spatio-temporal calculi. In COSIT.Google Scholar
Elidan, G. & Gould, S. 2008. Learning bounded treewidth Bayesian networks. In NIPS.Google Scholar
Frank, A. U. 1991. Qualitative spatial reasoning with cardinal directions. In ÖGAI.Google Scholar
Gantner, Z., Westphal, M. & Wölfl, S. 2008. GQR—a fast reasoner for binary qualitative constraint calculi. In AAAI Workshop on Spatial and Temporal Reasoning.Google Scholar
Garey, M. R., Johnson, D. S. & Stockmeyer, L. J. 1976. Some simplified NP-complete graph problems. Theoretical Computer Science 1, 237–267.Google Scholar
Goodwin, J., Dolbear, C. & Hart, G. 2008. Geographical linked data: the administrative geography of Great Britain on the semantic web. Transactions in GIS 12, 19–30.Google Scholar
Gottlob, G., Leone, N. & Scarcello, F. 2000. A comparison of structural CSP decomposition methods. Artificial Intelligence 124, 243–282.Google Scholar
Hazarika, S. M. 2012. Qualitative Spatio-Temporal Representation and Reasoning: Trends and Future Directions. IGI Global.Google Scholar
Huang, J. 2012. Compactness and its implications for qualitative spatial and temporal reasoning. In KR.Google Scholar
Huang, J., Li, J. J. & Renz, J. 2013. Decomposition and tractability in qualitative spatial and temporal reasoning. Artificial Intelligence 195, 140–164.Google Scholar
Jégou, P., Ndiaye, S. & Terrioux, C. 2005. Computing and exploiting tree-decompositions for solving constraint networks. In CP.Google Scholar
Jégou, P., Ndiaye, S. & Terrioux, C. 2006. An extension of complexity bounds and dynamic heuristics for tree-decompositions of CSP. In CP.Google Scholar
Jégou, P., Ndiaye, S. & Terrioux, C. 2007. Dynamic heuristics for backtrack search on tree-decomposition of CSPs. In IJCAI.Google Scholar
Jégou, P. & Terrioux, C. 2003. Hybrid backtracking bounded by tree-decomposition of constraint networks. Artificial Intelligence 146, 43–75.Google Scholar
Jégou, P. & Terrioux, C. 2014a. Bag-connected tree-width: a new parameter for graph decomposition. In ISAIM.Google Scholar
Jégou, P. & Terrioux, C. 2014b. Tree-decompositions with connected clusters for solving constraint networks. In CP.Google Scholar
Ladkin, P. B. & Maddux, R. D. 1994. On binary constraint problems. Journal of the ACM 41, 435–469.Google Scholar
Li, J. J., Huang, J. & Renz, J. 2009. A divide-and-conquer approach for solving interval algebra networks. In IJCAI.Google Scholar
Li, S., Long, Z., Liu, W., Duckham, M. & Both, A. 2015. On redundant topological constraints. Artificial Intelligence 225, 51–76.Google Scholar
Ligozat, G. 1998. Reasoning about cardinal directions. Journal of Visual Languages and Computing 9, 23–44.Google Scholar
Ligozat, G. 2011. Qualitative Spatial and Temporal Reasoning, Iste Series. Wiley.Google Scholar
Liu, W. & Li, S. 2012. Solving minimal constraint networks in qualitative spatial and temporal reasoning. In CP.Google Scholar
Lutz, C. & Milicic, M. 2007. A tableau algorithm for DLs with concrete domains and GCIs. Journal of Automated Reasoning 38, 227–259.Google Scholar
Montanari, U. 1974. Networks of constraints: fundamental properties and applications to picture processing. Information Sciences 7, 95–132.Google Scholar
Nebel, B. 1997. Solving hard qualitative temporal reasoning problems: evaluating the efficiency of using the ORD-Horn class. Constraints 1, 175–190.Google Scholar
Nebel, B. & Bürckert, H.-J. 1995. Reasoning about temporal relations: a maximal tractable subclass of Allen’s interval algebra. Journal of the ACM 42, 43–66.Google Scholar
Nikolaou, C. & Koubarakis, M. 2014. Fast consistency checking of very large real-world RCC-8 constraint networks using graph partitioning. In AAAI.Google Scholar
Randell, D. A., Cui, Z. & Cohn, A. 1992. A spatial logic based on regions and connection. In KR.Google Scholar
Renz, J. 1999. Maximal tractable fragments of the region connection calculus: a complete analysis. In IJCAI.Google Scholar
Renz, J. 2002a. A canonical model of the region connection calculus. Journal of Applied Non-Classical Logics 12, 469–494.Google Scholar
Renz, J. 2002b. Qualitative Spatial Reasoning with Topological Information. Springer-Verlag.Google Scholar
Renz, J. & Ligozat, G. 2005. Weak composition for qualitative spatial and temporal reasoning. In CP.Google Scholar
Renz, J. & Nebel, B. 1999. On the complexity of qualitative spatial reasoning: a maximal tractable fragment of the region connection calculus. Artificial Intelligence 108, 69–123.Google Scholar
Renz, J. & Nebel, B. 2001. Efficient methods for qualitative spatial reasoning. Journal of Artificial Intelligence Research 15, 289–318.Google Scholar
Sioutis, M. 2014. Triangulation versus graph partitioning for tackling large real world qualitative spatial networks. In ICTAI.Google Scholar
Sioutis, M. & Condotta, J.-F. 2014. Tackling large qualitative spatial networks of scale-free-like structure. In SETN.Google Scholar
Sioutis, M., Condotta, J.-F. & Koubarakis, M. 2016. An efficient approach for tackling large real world qualitative spatial networks. International Journal of Artificial Intelligence Tools 25, 1–33.Google Scholar
Sioutis, M. & Koubarakis, M. 2012. Consistency of chordal RCC-8 networks. In ICTAI.Google Scholar
Sioutis, M., Li, S. & Condotta, J.-F. 2015b. Efficiently characterizing non-redundant constraints in large real world qualitative spatial networks. In IJCAI.Google Scholar
Sioutis, M., Salhi, Y. & Condotta, J.-F. 2015c. A simple decomposition scheme for large real world qualitative constraint networks. In FLAIRS.Google Scholar
Sioutis, M., Salhi, Y. & Condotta, J.-F. 2015d. On the use and effect of graph decomposition in qualitative spatial and temporal reasoning. In SAC.Google Scholar
Tarjan, R. E. & Yannakakis, M. 1984. Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal on Computing 13, 566–579.Google Scholar
Tarski, A. 1941. On the calculus of relations. Journal of Symbolic Logic 6, 73–89.Google Scholar
Vilain, M., Kautz, H. & Beek, P. v. 1990. Readings in qualitative reasoning about physical systems. In Constraint Propagation Algorithms for Temporal Reasoning: A Revised Report, Weld, D. S. & de Kleer, J. (eds). Morgan Kaufmann Publishers Inc., 373–381.Google Scholar
Walsh, T. 2001. Search on high degree graphs. In IJCAI.Google Scholar
Westphal, M. & Hué, J. 2014. A concise Horn theory for RCC8. In ECAI.Google Scholar
Westphal, M., Hué, J. & Wölfl, S. 2013. On the propagation strength of SAT encodings for qualitative temporal reasoning. In ICTAI.Google Scholar
Westphal, M. & Wölfl, S. 2009. Qualitative CSP, finite CSP, and SAT: comparing methods for qualitative constraint-based reasoning. In IJCAI.Google Scholar
Yannakakis, M. 1981. Computing the minimum fill-in is NP-complete. SIAM Journal on Algebraic Discrete Methods 2, 77–79.Google Scholar