Use of graph theory to support map generalization

Cartography and Geographic Information Systems

Volumn 20, Issue 4, 1993, Pages 210-221

  Mackaness, William A ^a   Kate Beard, M ^a  

^a UNIVERSITY OF MAINE   (United States)

Author keywords

Automated map generalization; Graph theory; Network generalization

Indexed keywords

EID: 0038948873     PISSN: 10509844     EISSN: None     Source Type: Journal    
DOI: 10.1080/152304093782637479     Document Type: Article

References (35)

1. Aho, A.V., J.E. Hopcroft, and J.E. Ullman. 1974. The Design and Analysis of Computer Algorithms. Reading, Massachusetts: Addison Wesley.
2. Bollobas, B. 1979. Graph Theory: An Introductory Course. New York: Springer Verlag.
3. Borchert, J.R. 1961. The Twin Cities Urbanized Area: Past, Present, Future. Geographical Review, vol. 51, pp. 47-70.
4. Buttenfield, B.P., C.R. Weber, M. Leitner, J.J. Phelan, D.M. Ras-mussen, and G.R. Wright. 1991. How Does a Cartographic Object Behave? Computer Inventory of Topographic Maps. Proceedings of GIS/LIS ‘91, vol. 2, pp. 891-900.
5. Chartrand, G. 1977. Graphs as Mathematical Models. Boston: Prindle, Weber and Schmidt.
6. Chou, Y.-H. 1991. A Network Analysis of Domestic Airline Trans-portation in the United States. In Proceedings of GIS/LIS ‘91, vol.1, pp. 518-527.
7. Cliff, A.D., P. Haggett, and J.K. Ord. 1979. Graph Theory and Geography. In Applications of Graph Theory, R.J. Wilson and L.W. Beineke (eds.). London: Academic Press.
8. Corbett, J.P. 1979. Topological Principles in Cartography. U.S. De-partment of Commerce and the Bureau of the Census, Technical Paper 48; GPO stock no. 1980-311-046/1142. Washington, D.C.: U.S. Government Printing Office.
9. Haggett, P. 1990. Geography: A Modern Synthesis. New York: Harper Collins.
10. Hartsfield, N., and G. Ringel. 1990. Pearls in Graph Theory. Boston: Academic Press.
11. Herring, J.R. 1987. TIGRIS: Topologically Integrated Geographic Information System. In Proceedings of Auto Carto 8, Baltimore, vol. 1, pp. 282-291.
12. James, G.A., A.D. Cliff, and P. Haggett. 1970. Some Discrete Dis-tributions for Graphs with Applications to Regional Transport Networks. Geografiska Annaler, vol. 52B, pp. 14-21.
13. Keates, J.S. 1989. Cartographic Design and Production, second edition. London: Longman.
14. Konig, D. 1990. Theory of Finite and Infinite Graphs. Boston: Birkhauser.
15. Lichtner, W. 1979. Computer-Assisted Processes of Cartographic Generalization in Topographic Maps. Geo-Processing, vol. 1, pp. 183-199.
16. Mackaness, W.A. 1991. Integration and Evaluation of Map Gen-eralization. In Map Generalization: Making Rules for Knowledge Rep-resentation, B.P. Buttenfield and R.B. McMaster (eds.). London: Longman Group, pp. 217-226.
17. Maling, D.H. 1966. Foreword to Topfer, F., and W. Pillewitzer. 1966. The Principle of Selection. The Cartographic Journal, vol. 3, no. 1, pp. 10.
18. McMaster, R.B., and K.S. Shea. 1992. Generalization in Digital Car-tography. Resource Publications in Geography. Washington: As-sociation of American Geographers.
19. Muller, J.C. 1989. Theoretical Considerations for Automated Map Generalization. FTC Journal, vol. 3, no. 4, pp. 200-204.
20. Paiva, J.A.C., M.J. Egenhofer, and A.U. Frank. 1992. Spatial Reasoning about Flow Directions: Towards an Ontology for River Networks. In Proceedings of the 17th International Society for Pho-togrammetry and Remote Sensing Congress Meeting, XXIX, Part B3 Commission III, pp. 318-324. Washington: International Archives of Photogrammetry and Remote Sensing.
21. Rand McNally. 1991. Business Traveler’s Road Atlas. Boston: Rand McNally.
22. Ratajski, L. 1967. Ph£nom£nes des Points de Generalization. International Yearbook of Cartography, vol. 7, pp. 143-51.
23. Richardson, L.F. 1961. The Problem of Contiguity: An Appendix to the Statistics of Deadly Quarrels. General System Yearbook, vol. 6, pp. 139-187.
24. Robinson, A., R. Sale, J. Morison, and P.C. Muehrcke. 1984. Elements of Cartography, fifth edition. New York: John Wiley and Sons.
25. Rusak Mazur, E., and H.W. Castner. 1990. Horton’s Ordering Scheme and the Generalization of River Networks. The Cartographic Journal, vol. 27, pp. 104-112.
26. Sedgewick, R. 1992. Algorithms inC+ +. Reading, Massachusetts: Addison Wesley.
27. Strahler, A.N. 1960. Physical Geography. New York: John Wiley and Sons.
28. Switzer, R.M. 1975. Algebraic Topology-Homotopy and Homology. Berlin: Springer-Verlag.
29. Taaffe, E.J., R.L. Morrill, and P.R. Gould. 1963. Transport Expansion in Underdeveloped Countries: A Comparative Analysis. Geographical Review, vol. 53, pp. 503-529.
30. Tarjan, R.E. 1983. Data Structures and Network Algorithms. Philadelphia: Society for Industrial and Applied Mathematics.
31. Topfer, F., and W. Pillewizer. 1966. TTie Principles of Selection. Cartographic Journal, vol. 3, no. 1, pp. 10-16.
32. Temperley, H.N.V. 1981. Graph Theory and Applications. Chichester: Ellis Horwood.
33. White, M.S. 1978. A Geometrical Model for Error Detection and Correction. In Proceedings of Auto Carlo 3, vol. 1, pp. 439-456.
34. Williams, R.J. 1985. Enquiry Systems for the Interrogation of In-frastructure. In Proceedings of Auto Carto 7, vol. 1, pp. 572-581.
35. Wilson, R.J. 1979. Introduction to Graph Theory. London: Longman.