Abstract
Human beings use hierarchies extensively to simplify their conceptual models of reality and to perform reasoning more efficiently. Hierarchical structures are conceptually imposed on space and allow better performance of complex tasks in very large contexts. To understand how spatial hierarchies are formed and used is one of the most important questions in spatial reasoning research. In this project, wayfinding in large road networks is studied as a particular case. Humans can find fastest paths even in very large street networks quickly, applying a hierarchical strategy. Standard, non-hierarchical algorithms show performance that degrades rapidly with increasing network size. A hierarchical structure can be found as an abstraction from the hierarchy of street classes (expressway, highway, local road). This reduces the number of nodes involved in a search process, and allows to perform the search process in subnetworks more efficiently. We propose an algorithm which searches for an optimal path in the subgraph of the highest possible level. This leads to an efficient wayfinding algorithm, even where standard simple graph search algorithms for the shortest path become inadequate.
Work was partially supported by a grant from Intergraph Corporation.
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References
Ahuja, R.K., Thomas L. Magnanti, & J.B. Orlin: Network Flows: Thoery, Algorithms, and Applications. Englewood Cliffs, NJ: Prentice Hall, 1993.
Car, A. & A.U. Frank: “Hierarchical Street Networks as a Conceptual Model for Efficient Way Finding.” Proceedings of the EGIS'93 in Genova, Italy, 134–139, 1993.
Christaller, W.: Das Grundgeruest der raeumlichen Ordnung in Europa: die Systeme der europaeischen zentralen Orte. Vol. 24. Frankfurter geographische Hefte, Frankfurt am Main: Kramer, 1950.
Davis, E.: Representations of Commonsense Knowledge. Morgan Kaufmann Publishers, 1990.
De Floriani, L. & E. Puppo: “A Hierarchical Triangle-Based Model for Terrain Description.” In Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, ed. Frank, A.U., I. Campari, & U. Formentini. 236–251. Heidelberg-Berlin: Springer Verlag, 1992.
Dijkstra, E.W.: “A note on two problems in connection with graphs.” Numerische Mathematik (1, 1959): 269–271.
Erwig, M.: “Graphs in Spatial Databases.” Doctoral thesis, Fernuniversität Hagen, 1994.
Frederickson, G.N.: “Fast Algorithms for Shortest Paths in Planar Graphs, With Applications.” SIAM Journal on Computing 16 (6, 1987): 1004–1022.
Freksa, C.: “Qualitative Spatial Reasoning.” In Cognitive and Linguistic Aspects of Geographic Space, ed. Mark, D.M.& A.U. Frank. 361–372. 63. Kluwer Academic Press, 1991.
Gibbons, A.: Algorithmic Graph Theory. Cambridge University Press, 1985.
Gill, A.: Applied Algebra for the Computer Sciences. Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1976.
Golledge, R.G.: “Do People Understand Spatial Concepts: The Case of First-Order Primitives.” In Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, ed. Frank, A.U., I. Campari, & U. Formentini. 1–21. Heidelberg-Berlin: Springer Verlag, 1992.
Gopal, S., R.L. Klatzky, & T.R. Smith: “NAVIGATOR: A Psychologically Based Model of Environmental Learning Through Navigation.” Journal of Environmental Psychology (9, 1989): 309–331.
Gopal, S. & T.R. Smith: “Human Wayfinding in an Urban Environment: a Performance Analysis of a Computational Process Model.” Environment and Planning A 22 (1990): 169–191.
Güting, R.H.: “Extending a Spatial Database System by Graphs and Object Class Hierarchies.” Proceedings of the International Workshop on Database Management Systems for Geographical Applications, 16.–17.05.1991 in Capry, Italy, ESPRIT B.R.A. Working Group n.3191: “Basic GOODS: Basic Research Actions for Geographical Object-Oriented Databse Systems”, 103–124, 1991.
Hirtle, S.C. & P.B. Heidorn: “The Structure of Cognitive Maps: Representations and Processes.” In Behavior and Environment: Psychological and Geographical Approaches, ed. Gärling, T.& R.G. Golledge. 1–29, Chapter 7. 1992.
Hirtle, S.C. & J. Jonides: “Evidence of Hierarchies in Cognitive Maps.” Memory & Cognition 13 (3, 1985): 208–217.
Johnson, D.B.: “Efficient Algorithms for Shortest Paths in Sparse Networks.” Journal of the Association for Computing Machinery 24 (1, 1977): 1–13.
Knuth, D.E.: The Art of Computer Programming. Vol. 1. Reading MA: Addison-Wesley, 1973.
Kuipers, B.: “Modeling Spatial Knowledge.” Cognitive Science 2 (2, 1978): 129–154.
Kuipers, B.: “The Cognitive Map: Could it have been any other way?” In Spatial Orientation: Theory, Research and Application, ed. Pick, H.L.& L.P. Acredolo. 345–359. New York, NY: Plenum Press, 1983.
Kuipers, B.: “Spatial Reasoning.” Tutorial materials, 1992.
Kuipers, B. & T.S. Levitt: “Navigation and Mapping in Large-Scale Space.” AI Magazine 9 (2, 1988): 25–43.
Kuipers, B. et al.: “The Semantic Hierarchy in Robot Learning.” In Robot Learning, ed. Connell, J.& S. Mahadevan. Kluver Academic, 1993.
Lapalme, G. et al.: “GeoRoute.” Communications of the ACM 35 (1, 1992): 80–88.
Maass, W.: “A Cognitive Model for the Process of Multimodal Incremental Route Description.” In Spatial Information Theory: Theoretical Basis for GIS, ed. Frank, A.U.& I. Campari. 1–13. 716. Heidelberg-Berlin: Springer Verlag, 1993.
McNamara, T.P., J. K. Hardy, & S.C. Hirtle: “Subjective Hierarchies in Spatial Memory.” Journal of Environmental Psychology: Learning, Memory, and Cognition 15 (2, 1989): 211–227.
Palmer, E.S.: “Hierarchical Structure in Perceptual Representation.” Cognitive Psychology (9, 1977): 441–474.
Samet, H.: “The Quadtree and Related Hierarchical Data Structures.” ACM Computing Surveys 16 (2, 1984): 187–260.
Smyth, S.: “A Representational Framework for Route Planning in Space and Time.” Proceedings of the 5th International Symposium on Spatial Data Handling in Charleston, South Carolina, USA, 692–701, 1993.
Stevens, A. & P. Coupe: “Distortions in Judged Spatial Relations.” Cognitive Psychology (10, 1978): 422–437.
Stücklberger, A. & M. Wieser: “GIS und “Multilevel” — Routensuche.” Proceedings of the Grazer Geoinformatiktage '93 in Graz, Austria, ed. Bartelme, N., 49–55, 1993.
Timpf, S. et al.: “A Conceptual Model of Wayfinding Using Multiple Levels of Abstraction.” Proceedings of the GIS — form Space to Theory: Theories and Methods of Spatio-Temporal Reasoning in Pisa, Italy, ed. Frank, A.U., I. Campari, & U. Formentini, Springer Verlag, 348–367, 1992.
Wieser, M.: “Graphentheoretische Aspekte der Routenoptimierung.” Proceedings of the Angewandte Geoinformationstechnologie AGIT in Salzburg, 8, 1992.
Wirth, N.: Algorithms + Data Structures = Programs. Prentice Hall, Englewood Cliffs, N.J.: LB-Bibliothek, 1976.
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Car, A., Frank, A.U. (1994). Modelling a hierarchy of space applied to large road networks. In: Nievergelt, J., Roos, T., Schek, HJ., Widmayer, P. (eds) IGIS '94: Geographic Information Systems. IGIS 1994. Lecture Notes in Computer Science, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58795-0_30
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DOI: https://doi.org/10.1007/3-540-58795-0_30
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