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Explicit Graphs in a Functional Model for Spatial Databases
October 1994 (vol. 6 no. 5)
pp. 787-804

Observing that networks are ubiquitous in applications for spatial databases, we define a new data model and query language that especially supports graph structures. This model integrates concepts of functional data modeling with order-sorted algebra. Besides object and data type hierarchies, graphs are available as an explicit modeling tool, and graph operations are part of the query language. Graphs have three classes of components, namely, nodes, edges, and explicit paths. These are at the same time object types within the object type hierarchy and can be used like any other type. Explicit paths are useful because real-world objects often correspond to paths in a network. Furthermore, a dynamic generalization concept is introduced to handle heterogeneous collections of objects in a query. In connection with spatial data types, this leads to powerful modeling and querying capabilities for spatial databases, in particular for spatially embedded networks such as highways, rivers, public transport, and so forth. We use multilevel order-sorted algebra as a formal framework for the specification of our model. Roughly spoken, the first-level algebra defines types and operations of the query language, whereas the second-level algebra defines kinds (collections of types) and type constructors as functions between kinds, and so provides the types that can be used at the first level.

[1] D. J. Abel, "SIRO-DBMS: A database tool kit for geographical information systems,"Int. J. Geographical Inform. Syst., vol. 3, pp. 103-116, 1989.
[2] R. Agrawal, "Alpha: An Extension of Relational Algebra to Express a Class of Recursive Queries,"Proc. Third Int'l Conf. Data Eng., CS Press, Los Alamitos, Calif., Order No. FN762, 1987, pp. 580-590.
[3] F. Bancilhon, T. Briggs, S. Khoshafian, and P. Valduriez, "FAD: a powerful and simple database language," inProc. 13th VLDB Conf. (Brighton, UK), 1987, pp. 97-105.
[4] D. S. Batory, T. Y. Leung, and T. E. Wise, "Implementation concepts for an extensible data model and data language,"ACM TODS, vol. 13, no. 3, 1988.
[5] L. Becker and R.H. Güting, "Rule-based optimization and query processing in an extensible geometric database system,"ACM Trans. Database Syst.vol. 17, pp. 247-303, 1992.
[6] J. Biskup, U. Räsch, and H. Stiefeling, "An extension of SQL for querying graph relations,"Comput. Languages, vol. 15, pp. 65-82, 1990.
[7] V. Breazu-Tannen, P. Buneman, and A. Ohori, "Static type checking in object-oriented databases,"Data Eng., vol. 12, pp. 5-12, 1989.
[8] L. Cardelli, "Types for data oriented languages,"Int. Conf. Extending Database Technol., 1988, pp. 1-15.
[9] S. Cluet, C. Delobel, C. Lécluse, and P. Richard, "Reloop: An algebra based query language for an object-oriented database system,"1 st Int. Conf. Deductive and Object-Oriented Databases, 1989, pp. 294-313.
[10] I. F. Cruz, A. O. Mendelzon, and P. T. Wood, "G+: Recursive queries without recursion,"2nd Int. Conf. on Expert Database Syst., 1988, pp. 645-666.
[11] I. F. Cruz and T. S. Norvell, "Aggregative closure: An extension of transitive closure," inProc. IEEE 5th Int. Conf. Data Engineering, Los Angeles, CA, Feb. 1989.
[12] U. Dayal and J.M. Smith, "Probe: A knowledge-oriented database management system," in M.L. Brodie and J. Mylopoulos, Eds.,On Knowledge Base Management Systems. Berlin: Springer-Verlag, 1986.
[13] M. J. Egenhofer, "Spatial SQL: A query and presentation language,"IEEE Trans. Knowl. Data Eng., vol. 6, pp. 86-95, Feb. 1994.
[14] M. Erwig, "Encoding shortest paths in spatial networks," Tech. Rep. 116, FernUniversität Hagen, Germany, 1991.
[15] M. Erwig, "Graph algorithms = iteration + data structures? The structure of graph algorithms and a corresponding style of programming,"18th Int. Workshop on Graph-Theoretic Concepts in Comput. Sci., LNCS 657, pp. 277-292, 1992.
[16] M. Erwig, "Specifying type systems with multilevel order-sorted algebra,"3rd Int. Conf. on Algebraic Methodology and Software Technol., 1993, pp. 177-184.
[17] M. Erwig and R. H. Güting, "Explicit graphs in a functional model for spatial databases," Tech. Rep. 110, FernUniversität Hagen, Germany, 1991 (rev. version 1993).
[18] M. Erwig and U. W. Lipeck, "A functional DBPL revealing high level optimizations,"3rd Int. Workshop on Database Programming Languages, 1991, pp. 306-321.
[19] A. Frank, "MAPQUERY: Data base query language for retrieval of geometric data and their graphical representation,"Comput. Graphics., vol. 16, pp. 199-207, 1982.
[20] J. A. Goguen and J. Meseguer, "Order-sorted algebra I: Partial and overloaded operations, errors and inheritance," Tech. Rep., SRI Int., 1989.
[21] M. Gyssens, J. Paredaens, and D. Van Gucht, "A graph-oriented object database model," inProc. 9th ACM Symp. Principles of Database Syst., 1990, pp. 417-424.
[22] R. Güting, "Geo-relational algebra: a model and query language for geometric database systems," inProc. Int. Conf. Extending Database Technology, Venice, Italy, 1988, LNCS vol. 303. New York: Springer-Verlag, pp. 506-527.
[23] R. H. Güting, "Modeling nonstandard database systems by many-sorted algebras," Tech. Rep. 255, Fachbereich Informatik, Universität Dortmund, Germany, 1988.
[24] R. H. Güting, "Gral: An extensible relational database system for geometric applications,"15th Int. Conf. on Very Large Data Bases, 1989, pp. 33-44.
[25] R. H. Güting, "Extending a spatial database system by graphs and object class hierarchies," in G. Gambosi, H. Six, and M. Scholl, Eds.,Int. Workshop Database Mgmt. Syst. for Geographical Applic., Capri, France, 1991.
[26] R. H. Güting, "Second-order signature: A tool for specifying data models, query processing, and optimization,"ACM SIGMOD Conf. Mgmt. Data, 1993, pp. 277-286.
[27] R. H. Güting, R. Zicari, and D. M. Choy, "An algebra for structured office documents,"ACM Trans. Office Inform. Syst., vol. 7, pp. 123-157, 1989.
[28] T. Joseph and A. Cardenas, "PICQUERY: A high level query language for pictorial database management,"IEEE Trans. Software Eng., vol. 14, pp. 630-638, 1988.
[29] M. A. Hasan and V. K. Bhargava, "Division and bit-serial multiplication over GF(qm),"IEE Proc., part E, vol. 139, no. 3, pp. 230-236, May 1992.
[30] J. Leszczylowski and M. Wirsing, "Polymorphism, parameterization and typing: An algebraic specification perspective,"Symp. Theoretical Aspects of Comput. Sci., 1991, pp. 1-15.
[31] U. Lipeck and K. Neumann, "Modelling and Manipulating Objects in Geoscientific Databases,"5th Int. Conf. Entity-Relationship Approach, 1987, pp. 67-86.
[32] G. Lohman, "Grammar-like functional rules for representing query optimization alternatives,"ACM SIGMOD, 1988.
[33] M. Mainguenaud, "GROG: Geographical queries using graphs,"Advanced Database Syst. Symp., 1989.
[34] F. Manola and J. A. Orenstein, "Toward a general spatial data model for an object-oriented DBMS,"12th Int. Conf. Very Large Data Bases, 1986, pp. 328-335.
[35] P. E. Mantey and E. D. Carlson, "Integrated geographic data bases: The GADS experience," in A. Blaser, Ed.,Data Base Techniques for Pictorial Applications. Berlin, Germany: Springer, 1980, pp. 173-198.
[36] N. Nilsson,Principles of Artificial Intelligence. Palo Alto, CA: Tioga, 1980.
[37] T. Nipkow and C. Prehofer, "Type checking type classes,"20th Symp. Principles of Programming Languages, 1993, pp. 409-418.
[38] T. Nipkow and G. Snelting, "Type classes and overloading resolution via order-sorted unification,"Conf. Funct. Programming and Comput. Architecture, LNCS 523, 1991, pp. 1-14.
[39] A. Ohoriet al., "Database programming in Machiavelli--A polymorphic language with static type inference," inProc. ACM SIGMOD Conf., pp. 46-57, May 1989.
[40] J. A. Orenstein and F. Manola, "PROBE: Spatial data modeling and query processing in an image database application,"IEEE Trans. Software Eng., vol. 14, pp. 611-629, 1988.
[41] A. Poigné, "On specifications, theories, and models with higher types,"Inform. Control, vol. 68, pp. 1-46, 1986.
[42] A. Poulovassilis and P. King, "Extending the functional data model to computational completeness,"Int. Conf. on Extending Database Technol., 1990, pp. 75-91.
[43] A. Rosenthal, S. Heiler, U. Dayal, and F. Manola, "Traversal recursion: a practical approach to supporting recursive applications," inProc. 1986 ACM SIGMOD Conf.(Washington, DC), 1986, pp. 166-176.
[44] N. Rossopoulos, F. Faloutsos, and T. Sellis, "An efficient pictorial database system for PSQL,"IEEE Trans. Software Eng., vol. 14, pp. 639-650, 1988.
[45] M. Scholl and A. Voisard, "Thematic map modeling,"1 st Int. Symp. on Large Spatial Databases, 1989, pp. 167-190.
[46] D. Shipman, "The functional model and the data language daplex,"ACM Trans. Database Syst., vol. 6, no. 1, Mar. 1981.

Index Terms:
visual databases; database theory; graph theory; query languages; query processing; spatial databases; explicit graphs; functional model; data model; query language; graph structures; data modeling; order-sorted algebra; data type hierarchies; object hierarchies; explicit modeling tool; nodes; edges; explicit paths; object type hierarchy; dynamic generalization; spatial data types; spatially embedded networks; public transport; rivers; highways; multilevel order-sorted algebra
M. Erwig, R.H. Güting, "Explicit Graphs in a Functional Model for Spatial Databases," IEEE Transactions on Knowledge and Data Engineering, vol. 6, no. 5, pp. 787-804, Oct. 1994, doi:10.1109/69.317707
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