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Abstract: Exact implementations of algorithms of computational geometry are subject to exponential growth in running time and space. This exponential growth arises when the algorithms are cascaded: the output of one algorithm becomes the input to the next. Cascading is a significant problem in practice. We propose a geometric rounding technique: shortest path rounding. Shortest path rounding trades accuracy for space and time and eliminates the exponential cost introduced by cascading. It can be applied... (Update)
Context of citations to this paper: More
...et al. 2] improve the SR algorithms when many segments intersect in a pixel. Milenkovic presents a rounding scheme using shortest paths [8]. Three dimensional rounding algorithms have also been suggested and studied [1, 2, 7] 2 The Distance between a Vertex and a Non...
...et al. 8] improve the SR algorithms when many segments intersect in a pixel. Milenkovic presents a rounding scheme using shortest paths [14]. Three dimensional rounding algorithms of a similar nature have also been suggested and studied [7] 8] 13] The rest of the paper is...
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BibTeX entry: (Update)
V. Milenkovic, Shortest path geometric rounding, submitted. http://citeseer.ist.psu.edu/92651.html More
@article{ milenkovic00shortest,
author = "Victor Milenkovic",
title = "Shortest Path Geometric Rounding",
journal = "Algorithmica",
volume = "27",
number = "1",
pages = "57-86",
year = "2000",
url = "citeseer.ist.psu.edu/92651.html" }
Citations (may not include all citations):88 Linear-time algorithms for visibility and shortest path prob.. (context) - Guibas, Hershberger et al. - 1987
67 Verifiable implementations of geometric algorithms using fin.. (context) - Milenkovic - 1988
67 Verifiable Implementations of Geometric Algorithms using Fin.. (context) - Milenkovic - 1988
63 Efficient exact arithmetic for computational geometry - Fortune, Van Wyk - 1993
56 Finite-resolution computational geometry (context) - Greene, Yao - 1986
36 Double precision geometry: a general technique for calculati.. - Milenkovic - 1989
34 Translational polygon containment and minimal enclosure usin.. - Milenkovic, Daniels - 1995
34 Translational polygon containment and minimal enclosure usin.. - Milenkovic - 1996
33 Rounding arrangements dynamically - Guibas, Marimont - 1995
30 Numerical stability of algorithms for 2-d Delaunay triangula.. (context) - Fortune - 1995
27 Constructing strongly convex hulls using exact or rounded ar.. - Li, Milenkovic - 1992
25 Numerical stability of algorithms for line arrangements - Fortune, Milenkovic - 1991
24 A compaction algorithm for non-convex polygons and its appli.. (context) - Li, Milenkovic - 1993
22 Compaction algorithms for nonconvex polygons and their appli.. - Li - 1994
20 Practical segment intersection with finite precision output - Hobby
19 Containment algorithms for nonconvex polygons with applicati.. - Daniels - 1995
17 Finding compact coordinate representations for polygons and .. - Milenkovic, Nackman - 1990
15 special issue on Computational Geometry in Manufacturing (context) - Milenkovic, Containment et al.
15 special issue on Computational Geometry in Manufacturing (context) - Daniels, Milenkovic et al.
15 Robust adaptive floating-point geometric predicates (context) - Shewchuk - 1996
12 Practical methods for set operations on polygons using exact.. - Milenkovic - 1995
12 Rounding face lattices in the plane (context) - Milenkovic - 1989
11 Rounding face lattices in d dimensions (context) - Milenkovic - 1990
11 A solid modelling system free from topological inconsistency (context) - Sugihara, Iri - 1989
11 A rational rotation method for robust geometric algorithms (context) - Canny, Donald et al. - 1992
10 Center for Research in Computing Technology (context) - Daniels, Milenkovic et al. - 1994
10 Delaunay triangulations in three dimensions with finite prec.. (context) - Dey, Sugihara et al. - 1992
9 Column-based strip packing using ordered and compliant conta.. - Daniels, Milenkovic - 1996
8 A robust and consistent algorithm for intersecting convex po.. (context) - Sugihara - 1994
7 Integer line segment intersection (context) - Greene
6 Coordinate representation of order types requires exponentia.. (context) - Goodman, Pollack et al. - 1989
6 special issue on Uncertainties in Geometric Design (context) - Milenkovic, modeling et al. - 1993
5 Rational orthogonal approximations to orthogonal matrices - Milenkovic, Milenkovic - 1997
3 Numerically robust algorithm for contructing constrained Del.. (context) - Inagaki, Sugihara - 1994
2 Parallel robust algorithms for constructing strongly convex .. (context) - Chen, Wada et al. - 1996
2 Polygon nesting and robustness (context) - Bajaj, Dey - 1990
2 Volume II: Geometry (context) - Bachmann, Kunle et al. - 1974
1 Polyhedal modeling with multiprecision integer arithmetic (context) - Fortune - 1997
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