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Consistency of Chordal RCC-8 Networks

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This work was presented in the 24th IEEE International Conference on Tools with Artificial Intelligence

This work was presented in the 24th IEEE International Conference on Tools with Artificial Intelligence


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  • 1. Consistency of Chordal RCC-8 Networks Michael Sioutis Consistency of Chordal RCC-8 NetworksOutlineIntroductionPyRCC8 Michael Sioutis -PathConsistency Department of Informatics and TelecommunicationsExperimentalResults National and Kapodistrian University of AthensConclusionsFuture Work November 8, 2012AcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 2. Table of Contents Consistency of Chordal RCC-8 Networks 1 Introduction Michael Sioutis 2 PyRCC8OutlineIntroductionPyRCC8 3 -Path Consistency -PathConsistency 4 Experimental ResultsExperimentalResultsConclusions 5 ConclusionsFuture WorkAcknowledge 6 Future WorkBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 3. What is Qualitative Spatial Reasoning? Consistency of Chordal RCC-8 Networks Michael SioutisOutline Qualitative spatial reasoning is based on qualitativeIntroductionPyRCC8 abstractions of spatial aspects of the common-sense -Path background knowledge, on which our human perspectiveConsistency on the physical reality is basedExperimentalResultsConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 4. Reasons for Qualitative Spatial Reasoning Consistency of Chordal RCC-8 Networks Michael SioutisOutline Two main reasons why non-precise, qualitative spatialIntroduction information may be useful:PyRCC8 1 Only partial information may be available -PathConsistency 2 Spatial constraints are often most naturally stated inExperimental qualitative termsResultsConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 5. Applications of Qualitative Spatial Reasoning Consistency of Chordal RCC-8 Networks Michael Sioutis Qualitative spatial reasoning is an important subproblemOutline in many applications, such as:IntroductionPyRCC8 Robotic navigation -Path High level visionConsistency Geographical information systems (GIS)Experimental Reasoning and querying with semantic geospatial queryResults languages (e.g., stSPARQL, GeoSPARQL)ConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 6. Region Connection Calculus Consistency of Chordal RCC-8 Networks Michael SioutisOutline The Region Connection Calculus (RCC) is a first-orderIntroduction language for representation of and reasoning aboutPyRCC8 topological relationships between extended spatial regions -Path RCC abstractly describes regions, that are non-emptyConsistencyExperimental regural subsets of some topological space which do notResults have to be internally connectedConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 7. The RCC-8 Calculus Consistency of Chordal RCC-8 Networks Michael RCC-8 is a constraint language formed by the combination Sioutis of the following eight jointly exhaustive and pairwiseOutline disjoint base relations:Introduction disconnected (DC)PyRCC8 externally connected (EC) -PathConsistency equal (EQ) partially overlapping (PO)ExperimentalResults tangential proper part (TPP)Conclusions tangential proper part inverse (TPPi)Future Work non-tangential proper part (NTPP)Acknowledge non-tangential proper part inverse (NTPPi)Bibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 8. The Eight Basic Relations of the RCC-8 Calculus Consistency of Chordal RCC-8 Networks Michael Y Y X Y X Y Sioutis X X X DC Y X EC Y X TPP Y X NTPP YOutlineIntroduction X X X X Y Y YPyRCC8 Y -Path X PO Y X EQ Y X TPPi Y X NTPPi YConsistencyExperimental Figure: Two dimesional examples for the eight base relations of RCC-8ResultsConclusionsFuture Work From these basic relations, combinations can be built. ForAcknowledge example, proper part (PP) is the union of TPP and NTPP.Bibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 9. The RCC-8 Composition Table Consistency of Chordal DC EC PO TPP NTPP TPPi NTPPi EQ RCC-8 DC,EC DC,EC DC,EC DC,EC Networks DC * PO,TPP PO,TPP PO,TPP PO,TPP DC DC DC NTPP NTPP NTPP NTPP Michael DC,EC DC,EC DC,EC EC,PO PO Sioutis EC PO,TPPi PO,TPP PO,TPP TPP TPP DC,EC DC EC NTPPi TPPi,EQ NTPP NTPP NTPPOutline DC,EC DC,EC PO PO DC,EC DC,EC PO PO,TPPi PO,TPPi * TPP TPP PO,TPPi PO,TPPi POIntroduction NTPPi NTPPi NTPP NTPP NTPPi NTPPi DC,EC TPP DC,EC DC,ECPyRCC8 TPP DC DC,EC PO,TPP NTPP NTPP PO,TPP PO,TPPi TPP -Path NTPP TPPi,EQ NTPPiConsistency DC,EC DC,EC NTPP DC DC PO,TPP NTPP NTPP PO,TPP * NTPPExperimental NTPP NTPPResults DC,EC EC,PO PO PO,EQ PO TPPi TPPi PO,TPPi TPPi TPPi TPP TPP NTPPi NTPPi TPPiConclusions NTPPi NTPPi NTPPi TPPi NTPP DC,EC PO PO PO PO,TPPFuture Work NTPPi PO TPPi TPPi TPPi NTPP NTPPi NTPPi NTPPiAcknowledge TPPi NTPPi NTPPi NTPPi NTPPi NTPPi TPPi,EQBibliography EQ DC EC PO TPP NTPP TPPi NTPPi EQ Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 10. The RSAT Reasoning Problem Consistency of Chordal RCC-8 Networks Michael Sioutis RSAT in the RCC-8 framework is the reasoning problem ofOutline deciding whether there is a spatial configuration where theIntroduction relations between the regions can be described by a spatialPyRCC8 formula Θ -PathConsistency RSAT is NP-Complete!Experimental ˆ However, tractable subsets S of RCC-8 exist, such as H8 ,Results C8 , Q8 [5], for which the consistency problem can beConclusions decided in polynomial timeFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 11. The RSAT Reasoning Problem Consistency of Chordal RCC-8 Networks Michael Sioutis RSAT in the RCC-8 framework is the reasoning problem ofOutline deciding whether there is a spatial configuration where theIntroduction relations between the regions can be described by a spatialPyRCC8 formula Θ -PathConsistency RSAT is NP-Complete!Experimental ˆ However, tractable subsets S of RCC-8 exist, such as H8 ,Results C8 , Q8 [5], for which the consistency problem can beConclusions decided in polynomial timeFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 12. The RSAT Reasoning Problem Consistency of Chordal RCC-8 Networks Michael Sioutis RSAT in the RCC-8 framework is the reasoning problem ofOutline deciding whether there is a spatial configuration where theIntroduction relations between the regions can be described by a spatialPyRCC8 formula Θ -PathConsistency RSAT is NP-Complete!Experimental ˆ However, tractable subsets S of RCC-8 exist, such as H8 ,Results C8 , Q8 [5], for which the consistency problem can beConclusions decided in polynomial timeFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 13. Path Concistency Consistency of Chordal RCC-8 Networks Approximates consistency and realizes forward checking in Michael Sioutis a backtracking algorithmOutline Checks the consistency of triples of relations andIntroduction eliminates relations that are impossible though iteravelyPyRCC8 performing the operation -PathConsistency Rij ← Rij ∩ Rik RkjExperimentalResults until a fixed point R is reachedConclusions If Rij = ∅ for a pair (i, j) then R is inconsistent, otherwiseFuture Work R is path-consistent.Acknowledge Computing R is done in O(n3 )Bibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 14. About PyRCC8.. Consistency of Chordal RCC-8 Networks PyRCC81 is an efficient qualitative spatial reasoner written Michael Sioutis in pure Python. It employs PyPy2 , a fast, compliant implementation of the Python 2 languageOutlineIntroductionPyRCC8 -PathConsistencyExperimentalResults PyRCC8 offers a path consistency algorithm for solvingConclusions tractable RCC-8 networks and a backtracking-basedFuture Work algorithm for general networksAcknowledgeBibliography 1 http://pypi.python.org/pypi/PyRCC8 2 http://pypy.org/ Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 15. Comparing PC Implementations of Different Reasoners Consistency of Chordal RCC-8 Networks We compare the PC implementation of PyRCC8 to the PC Michael implementations of the following qualitative spatial Sioutis reasoners:Outline Renz’s solver3Introduction GQR4PyRCC8 Pellet Spatial5 -PathConsistency The admingeo6 dataset (11761 regions / 77910 relations)ExperimentalResults was used which was properly translated to fit the inputConclusions format of the different PC implementationsFuture WorkAcknowledge 3Bibliography http://users.rsise.anu.edu.au/%7Ejrenz/software/rcc8-csp-solving.tar.gz 4 http://sfbtr8.informatik.uni-freiburg.de/R4LogoSpace/Tools/gqr.html 5 http://clarkparsia.com/pellet/spatial/ 6 http://data.ordnancesurvey.co.uk/ontology/admingeo/ Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 16. Evaluation with a Large Dataset Consistency of Chordal RCC-8 Networks Performance of four QSRs for the admingeo dataset 105 Michael Sioutis 104Outline 103Introduction 102 CPU time (sec)PyRCC8 -Path 101ConsistencyExperimental 100Results 10-1 RenzConclusions PyRCC8Future Work 10 -2 GQR Pellet-SpatialAcknowledge 10-3 0 10000 20000 30000 40000 50000 60000 70000Bibliography Number of relations Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 17. Consistency Consistency of Chordal RCC-8 Networks Michael Sioutis To explore the search space for the general case of RCC-8OutlineIntroduction networks in order to solve an instance Θ of RSAT, somePyRCC8 sort of backtracking must be used -Path We implemented two backtracking algorithms:ConsistencyExperimental 1 A strictly recursive oneResults 2 An equivalent iterative one which resembles recursionConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 18. Comparing PyRCC8 to Other Reasoners Consistency of Chordal RCC-8 Networks Michael Sioutis We compare PyRCC8 to the following qualitative spatialOutline reasoners:Introduction Renz’s solver7PyRCC8 GQR8 -PathConsistency Different size n of instances from A(n, d = 9.5, l = 4.0)ExperimentalResults were usedConclusionsFuture WorkAcknowledgeBibliography 7 http://users.rsise.anu.edu.au/%7Ejrenz/software/rcc8-csp-solving.tar.gz 8 http://sfbtr8.informatik.uni-freiburg.de/R4LogoSpace/Tools/gqr.html Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 19. Comparison Diagram Consistency of Chordal RCC-8 Networks Performance of three QSRs for A(n,d=9.5,l=4.0) 102 Michael Renz Sioutis PyRCC8 GQROutline 101Introduction CPU time (sec)PyRCC8 -Path 100ConsistencyExperimentalResults 10-1ConclusionsFuture WorkAcknowledge 10-2 100 200 300 400 500 600 700 800 900Bibliography Number of nodes Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 20. -Path Concistency Consistency of Chordal RCC-8 Networks Michael SioutisOutline Up till now, all aproaches in qualitative spatial reasoningIntroduction enforce path consistency on a complete spatial networkPyRCC8 We propose enforcing path consistency on a chordal -Path spatial network [2] as Chmeiss and Condotta have done forConsistencyExperimental temporal networks [3], and we call this type of localResults consistency as -path consistency for clarityConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 21. -Path Concistency Consistency of Chordal RCC-8 Networks Michael SioutisOutline Up till now, all aproaches in qualitative spatial reasoningIntroduction enforce path consistency on a complete spatial networkPyRCC8 We propose enforcing path consistency on a chordal -Path spatial network [2] as Chmeiss and Condotta have done forConsistencyExperimental temporal networks [3], and we call this type of localResults consistency as -path consistency for clarityConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 22. Chordal Graph Consistency of Chordal RCC-8 A graph is chordal if each of its cycles of four or more Networks nodes has a chord, which is an edge joining two nodes Michael Sioutis that are not adjacent in the cycle An example of a chordal graph is shown below:OutlineIntroductionPyRCC8 -PathConsistencyExperimentalResultsConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 23. Triangulation Consistency of Chordal RCC-8 Networks Michael Triangulation of a given graph is done by eliminating the Sioutis vertices one by one and connecting all vertices in theOutline neighbourhood of each eliminated vertex with fill edgesIntroductionPyRCC8 Determining a minimum triangulation is an NP-hard -Path problemConsistency Use of several heuristics for sub-optimal solutions (e.g.ExperimentalResults minimum degree, minimum fill)Conclusions Chordality checking can be done efficiently in O(|V | + |E |)Future Work time, for a graph G = (V , E ) (e.g., with MCS, LexBFS)AcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 24. Preliminaries Consistency of Chordal RCC-8 Networks Michael Sioutis Let G = (V , E ) be an undirected chordal graph. ThereOutline exists a tree T , called a clique tree of G , whose vertex setIntroduction is the set of maximal cliques of GPyRCC8 -Path Let C be a constraint network from a given CSP. Then,Consistency VC refers to the set of variables of CExperimentalResults If V is any set of variables, CV will be the constraintConclusions network C that involves variables of VFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 25. Patchwork Property in RCC-8 Networks Consistency of Chordal RCC-8 Networks Michael Sioutis DefinitionOutline We will say that a CSP has the patchwork property if for anyIntroduction finite satisfiable constraint networks C and C of the CSP suchPyRCC8 that CVC ∩VC = C VC ∩VC , the constraint network C ∪ C is -Path satisfiable [4].ConsistencyExperimentalResults PropositionConclusions ˆ The three CSPs for path consistent H8 , C8 , and Q8 networks,Future Work respectively, all have patchwork [4].AcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 26. Proposition Consistency of Chordal RCC-8 Networks Michael Sioutis PropositionOutlineIntroduction Let C be an RCC-8 constraint network with relations fromPyRCC8 ˆ H8 , C8 , and Q8 on its edges. Let G be the chordal graph that -Path results from triangulating the associated constraint graph of C ,ConsistencyExperimental and T a clique tree of G . C is consistent if all the networksResults corresponding to the nodes of T are path consistent.ConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 27. Example Consistency of Chordal RCC-8 Networks v1 v2 v1 v2 Michael Sioutis (a)Outline v5 (b) v5IntroductionPyRCC8 v3 v4 v3 v4 -Path v1 v2 v2 v2Consistency {v1, v2, v3}Experimental {v2 , v3 }Results (c) v5 {v2, v3, v4}Conclusions {v2 , v4 }Future Work v3 v3 v4 {v2, v4, v5} v4AcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 28. PyRCC8 Consistency of Chordal RCC-8 Networks Michael SioutisOutline PyRCC8 is a chordal reasoner which was developed byIntroduction extending PyRCC8PyRCC8 Similarly to PyRCC8, PyRCC8 offers a -path -PathConsistency consistency algorithm for solving tractable RCC-8 networksExperimental and a backtracking-based algorithm for general networksResultsConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 29. -Path Consistency Algorithm Consistency of Chordal RCC-8 -Path-Consistency(C, G) Networks Input: A constraint network C and its chordal graph G Michael Output: True or False Sioutis 1: Q ← {(i, j) | (i, j) ∈ E } // Initialize the queue 2: while Q is not empty doOutline 3: select and delete an (i, j) from Q 4: for each k such that (i, k), (k, j) ∈ E doIntroduction 5: t ← Cik ∩ (Cij Cjk ) 6: if t = Cik thenPyRCC8 7: if t = ∅ then -Path 8: return FalseConsistency 9: Cik ← t 10: Cki ← ˘ tExperimental 11: Q ← Q ∪ {(i, k)}Results 12: t ← Ckj ∩ (Cki Cij ) 13: if t = Ckj thenConclusions 14: if t = ∅ then 15: return FalseFuture Work 16: Ckj ← tAcknowledge 17: Cjk ← ˘ t 18: Q ← Q ∪ {(k, j)}Bibliography 19:return True Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 30. Complexity Analysis Consistency of Chordal RCC-8 Networks Michael Let δ denote the maximum degree of a vertex of G Sioutis For each arc (i, j) selected at line 3, we have at most δOutline vertices of G corresponding to index k such that vi , vj , vkIntroduction forms a trianglePyRCC8 -Path Additionaly, there exist |E | arcs in the network and oneConsistency can remove at most |B|9 values from any relation thatExperimentalResults corresponds to an arcConclusions It results that the time complexity of -path consistencyFuture Work is O(δ · |E | · |B|)AcknowledgeBibliography 9 B refers to the set of base relations of RCC-8 Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 31. Recursive -Consistency Algorithm Consistency of Chordal RCC-8 Networks Michael -Consistency(C, G) Sioutis Input: A constraint network C and its chordal graph G Output: A refined constraint network C’ if C is satisfiable or NoneOutline 1: if not -Path-Consistency(C, G) thenIntroduction 2: return None 3: if no constraint can be split thenPyRCC8 4: return C 5: else -Path 6: choose unprocessed constraint xi Rxj ; split R into S1 , ..., Sk ∈ S: S1 ∪ ... ∪ Sk = RConsistency 7: Values ← {Sl | 1 ≤ l ≤ k} 8: for V in Values doExperimental 9: replace xi Rxj with xi Vxj in CResults 10: result = -Consistency(C, G) 11: if result = None thenConclusions 12: return resultFuture Work 13: return NoneAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 32. Iterative -Consistency Algorithm Consistency of Chordal -Consistency(C, G) RCC-8 Input: A constraint network C, A chordal graph G Networks Output: A refined constraint network C’ if C is satisfiable or None Michael 1: Stack ← {} // Initialize stack Sioutis 2: if not -Path-Consistency(C, G) then 3: return None 4: while 1 doOutline 5: if no constraint can be split thenIntroduction 6: return C 7: elsePyRCC8 8: choose unprocessed constraint xi Rxj ; split R into S1 , ..., Sk ∈ S: S1 ∪ ... ∪ Sk = R 9: Values ← {Sl | 1 ≤ l ≤ k} -Path 10: while 1 doConsistency 11: if not Values then 12: while Stack doExperimental 13: C, Values = Stack.pop()Results 14: if Values then 15: breakConclusions 16: elseFuture Work 17: return None 18: V = Values.pop()Acknowledge 19: replace xi Rxj with xi Vxj in C 20: if -Path-Consistency(C, G) thenBibliography 21: break 22: Stack.push(C, Values) 23:raise RuntimeError, Can’t happen Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 33. Comparing PyRCC8 to PyRCC8 Consistency of Chordal RCC-8 Networks Michael SioutisOutline We compare PyRCC8 to PyRCC8, a complete graphIntroduction dedicated reasoner, using the following data:PyRCC8 Random instances composed from the set of all RCC-8 -PathConsistency relationsExperimental The admingeo10 datasetResultsConclusionsFuture WorkAcknowledgeBibliography 10 http://data.ordnancesurvey.co.uk/ontology/admingeo/ Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 34. Experimenting with Random Instances Consistency of Chordal RCC-8 Networks Michael Sioutis We generated instances from A(100, d, l = 4.0), for d varying from 3 to 15 with a step of 0.5. For each series,OutlineIntroduction 300 networks were generated using Renz’s networkPyRCC8 generator11 -Path We used the Horn relations set as our split set, and theConsistency dynamic/local constraint scheme with a weighted queueExperimentalResults configuration, since it proved to be the best combinationConclusions for both reasoners, confirming the results in [5]Future WorkAcknowledgeBibliography 11 http://users.rsise.anu.edu.au/%7Ejrenz/software/rcc8-csp-solving.tar.gz Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 35. Comparison Diagram on CPU time Consistency of Chordal RCC-8 Networks Performance of function Consistency for A(100,d,l=4.0) 0.70 Michael PyRCC8 Sioutis 0.65 PyRCC8Outline 0.60Introduction CPU time (sec)PyRCC8 0.55 -PathConsistency 0.50ExperimentalResults 0.45Conclusions 0.40Future WorkAcknowledge 0.35 4 6 8 10 12 14Bibliography Average degree of network for non trivial constraints Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 36. Comparison Diagram on # of Revised Arcs Consistency of Chordal RCC-8 Networks Performance of function Consistency for A(100,d,l=4.0) 3000 Michael PyRCC8 Sioutis PyRCC8 2500OutlineIntroduction 2000 # of revised arcsPyRCC8 -Path 1500ConsistencyExperimental 1000ResultsConclusions 500Future WorkAcknowledge 0 4 6 8 10 12 14Bibliography Average degree of network for non trivial constraints Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 37. Comparison Diagram on # of Checked Constraints Consistency of Chordal RCC-8 Networks Performance of function Consistency for A(100,d,l=4.0) 300000 Michael PyRCC8 Sioutis PyRCC8 250000Outline # of consistency checksIntroduction 200000PyRCC8 -Path 150000ConsistencyExperimental 100000ResultsConclusions 50000Future WorkAcknowledge 0 4 6 8 10 12 14Bibliography Average degree of network for non trivial constraints Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 38. Results Summary Consistency of Chordal RCC-8 Networks Michael SioutisOutline PyRCC8 PyRCC8 %Introduction CPU time 0.524s 0.509s 2.80%PyRCC8 revised arcs 1300.681 801.204 38.40% -Path checked constraints 105751.173 74864.985 29.21%ConsistencyExperimental Table: Comparison based on the average of different parametersResultsConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 39. Experimenting with the Admingeo Dataset Consistency of Chordal RCC-8 Networks Michael Sioutis The admingeo12 dataset consists of 11761 regions andOutline 77910 base relations, thus being an extremely large andIntroduction sparse network, making itself a good candidate for stressPyRCC8 testing different path consistency implementations -PathConsistency We used a simple queue configuration, since the weightedExperimental variants made no difference on this dataset other thanResults using much more memoryConclusionsFuture WorkAcknowledgeBibliography 12 http://data.ordnancesurvey.co.uk/ontology/admingeo/ Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 40. Comparison Diagram on CPU Time Consistency of Chordal RCC-8 Networks Performance of function PC for the admingeo dataset 105 Michael PyRCC8 Sioutis PyRCC8 104OutlineIntroduction 103 CPU time (sec)PyRCC8 -Path 102ConsistencyExperimental 101ResultsConclusions 100Future WorkAcknowledge 10-1 0 10000 20000 30000 40000 50000 60000 70000Bibliography Number of relations Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 41. Comparison Diagram on # of Revised Arcs Consistency of Chordal RCC-8 Networks Performance of function PC for the admingeo dataset 108 Michael PyRCC8 Sioutis 107 PyRCC8Outline 106Introduction # of revised arcsPyRCC8 105 -PathConsistency 104ExperimentalResults 103ConclusionsFuture Work 102Acknowledge 101 0 10000 20000 30000 40000 50000 60000 70000Bibliography Number of relations Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 42. Comparison Diagram on # of Checked Constraints Consistency of Chordal RCC-8 Networks Performance of function PC for the admingeo dataset 1012 Michael PyRCC8 Sioutis 1011 PyRCC8 1010Outline 109 # of consistency checksIntroductionPyRCC8 108 -Path 107Consistency 106ExperimentalResults 105Conclusions 104Future Work 103Acknowledge 102 0 10000 20000 30000 40000 50000 60000 70000Bibliography Number of relations Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 43. Results Summary Consistency of Chordal RCC-8 Networks Michael SioutisOutline PyRCC8 PyRCC8 %Introduction CPU time 1825.129s 289.203s 84.15%PyRCC8 revised arcs 4834133.78 373080.28 92.28% -Path checked constraints 3.606e + 10 1.181e + 09 96.72%ConsistencyExperimental Table: Comparison based on the average of different parametersResultsConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 44. Test Machine Consistency of Chordal RCC-8 Networks Michael All experiments were carried out on a computer with an Sioutis Intel Xeon 4 Core X3220 processor with a CPU frequencyOutline of 2.40 GHz, 8 GB RAM, and the Debian Lenny x86 64 OSIntroduction Renz’s solver and GQR were compiled with gcc/g++ 4.4.3PyRCC8 -Path PelletSpatial was run with OpenJDK 6 build 19, whichConsistency implements Java SE 6ExperimentalResults PyRCC8 was run with PyPy 1.8, which implementsConclusions Python 2.7.2Future Work Only one of the CPU cores was used for the experimentsAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 45. Conclusions Consistency of Chordal RCC-8 We made the case for a new generation of RCC-8 Networks reasoners implemented in Python, and making use of Michael Sioutis advanced Python environments, such as PyPy, utilizing trace-based JIT compilation techniquesOutlineIntroduction We introduced -path consistency for RCC-8 networksPyRCC8 We showed that -path consistency is sufficient to decide -PathConsistency the consistency problem for the maximal tractable subsets ˆ H8 , C8 , and Q8 of RCC-8ExperimentalResults We implemented a chordal graph dedicated reasoner forConclusionsFuture Work RCC-8 networksAcknowledge We showed expirimentally that -path consistency canBibliography offer a great advantage over full path consistency on sparse graphs Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 46. Main Points Consistency of Chordal RCC-8 Networks Michael Explore self learning heuristics regarding variable and value Sioutis selectionOutline Create module to generate spatial CSPsIntroduction Transform PyRCC8 into a generic qualitative reasonerPyRCC8 -Path Use other methods of triangulation and compare theConsistency behavior of partial path consistency for these differentExperimentalResults methodsConclusions Perform experiments with other possible real datasets,Future Work such as GADM13AcknowledgeBibliography 13 http://gadm.geovocab.org/ Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 47. Acknowledge Consistency of Chordal RCC-8 Networks Michael SioutisOutline This work was funded by the FP7 project TELEIOSIntroduction (257662)PyRCC8 I would also like to thank my colleagues, and Katia -PathConsistency Papakonstantinopoulou especially, for their help, interest,Experimental and adviceResultsConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 48. References Consistency of Chordal RCC-8 [Van Beek and Manchak] Networks The design and experimental analysis of algorithms for temporal reasoning Michael JAIR, vol. 4, pages 1–18, 1996 Sioutis [Bliek and Sam-Haroud]Outline Path Consistency on Triangulated Constraint GraphsIntroduction In IJCAI, 1999PyRCC8 [Chmeiss and Condotta] -Path Consistency of Triangulated Temporal Qualitative Constraint NetworksConsistency In ICTAI, 2011Experimental [Huang]Results Compactness and Its Implications for Qualitative Spatial and TemporalConclusions ReasoningFuture Work In KR, 2012Acknowledge [Renz and Nebel]Bibliography Efficient Methods for Qualitative Spatial Reasoning JAIR, vol. 15, pages 289–318, 2001 Michael Sioutis Consistency of Chordal RCC-8 Networks
  • 49. The End Consistency of Chordal RCC-8 Networks Michael SioutisOutlineIntroductionPyRCC8 Any Questions? -PathConsistencyExperimentalResultsConclusionsFuture WorkAcknowledgeBibliography Michael Sioutis Consistency of Chordal RCC-8 Networks