Abstract
We develop algorithms to compute Voronoi diagrams, shortest path maps, and the Fréchet distance in the plane with polygonal obstacles. Distances between points are measured either by link distance or by Euclidean shortest path distance.
This work has been supported by the National Science Foundation grant NSF CAREER CCF-0643597. Previous versions of this work have appeared as technical reports [6,7].
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References
Agarwal, P.K., Sharir, M.: Davenport–Schinzel Sequences and Their Geometric Applications. In: Handbook of Computational Geometry, pp. 1–47. Elsevier, Amsterdam (2000)
Alt, H., Godau, M.: Computing the Fréchet distance between two polygonal curves. International Journal of Computational Geometry and Applications 5, 75–91 (1995)
Arkin, E.M., Mitchell, J.S.B., Suri, S.: Optimal link path queries in a simple polygon. In: 3rd Symposium on Discrete Algorithms (SODA), pp. 269–279 (1992)
Chiang, Y., Mitchell, J.S.B.: Two-point Euclidean shortest path queries in the plane. In: 10th Symposium on Discrete Algorithms (SODA), pp. 215–224 (1999)
Cook IV, A.F., Wenk, C.: Geodesic Fréchet distance inside a simple polygon. In: 25th Symposium on Theoretical Aspects of Computer Science (STACS) (2008)
Cook IV, A.F., Wenk, C.: Geodesic Fréchet distance with polygonal obstacles. Technical Report CS-TR-2008-010, University of Texas at San Antonio (2008)
Cook IV, A.F., Wenk, C.: Min-link shortest path maps and Fréchet distance. Technical Report CS-TR-2008-011, University of Texas at San Antonio (2008)
Dumitrescu, A., Rote, G.: On the Fréchet distance of a set of curves. In: 16th Canadian Conference on Computational Geometry (CCCG), pp. 162–165 (2004)
Efrat, A., Guibas, L.J., Har-Peled, S., Lin, D.C., Mitchell, J.S.B., Murali, T.M.: Sweeping simple polygons with a chain of guards. In: 11th Symposium on Discrete Algorithms (SODA), pp. 927–936 (2000)
Gewali, L., Meng, A., Mitchell, J.S.B., Ntafos, S.: Path planning in 0/1/∞ weighted regions with applications. In: 4th Symposium on Computational Geometry (SoCG), pp. 266–278 (1988)
Guibas, L.J., Hershberger, J., Leven, D., Sharir, M., Tarjan, R.E.: Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica 2, 209–233 (1987)
Henzinger, M.R., Klein, P., Rao, S., Subramanian, S.: Faster shortest-path algorithms for planar graphs. Journal of Computer and System Sciences 55(1), 3–23 (1997)
Hershberger, J., Suri, S.: An optimal algorithm for Euclidean shortest paths in the plane. SIAM Journal on Computing 28(6), 2215–2256 (1999)
Maheshwari, A., Sack, J.-R., Djidjev, H.N.: Link distance problems. In: Handbook of Computational Geometry (1999)
Mitchell, J.S.B.: Geometric shortest paths and network optimization. In: Handbook of Computational Geometry (1998)
Mitchell, J.S.B., Rote, G., Woeginger, G.J.: Minimum-link paths among obstacles in the plane. In: 6th Symposium on Computational Geometry (SoCG), pp. 63–72 (1990)
Suri, S.: A linear time algorithm for minimum link paths inside a simple polygon. Computer Vision and Graphical Image Processing (CVGIP) 35(1), 99–110 (1986)
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Cook, A.F., Wenk, C. (2009). Link Distance and Shortest Path Problems in the Plane. In: Goldberg, A.V., Zhou, Y. (eds) Algorithmic Aspects in Information and Management. AAIM 2009. Lecture Notes in Computer Science, vol 5564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02158-9_13
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DOI: https://doi.org/10.1007/978-3-642-02158-9_13
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