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ABSTRACT
A compendium of thirty previously published open problems in computational geometry is presented
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
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1
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N. Amenta , S. Choi , T. K. Dey , N. Leekha, A simple algorithm for homeomorphic surface reconstruction, Proceedings of the sixteenth annual symposium on Computational geometry, p.213-222, June 12-14, 2000, Clear Water Bay, Kowloon, Hong Kong
[doi> 10.1145/336154.336207]
|
| |
2
|
|
| |
3
|
|
| |
4
|
G. Albers, L. J. Guibas, J. S. B. Mitchell, and T. Roos. Voronoi diagrams of moving points. Internat. J. Comput. Geom. Appl., 8:365-380, 1998.
|
 |
5
|
Nancy M. Amato , Michael T. Goodrich , Edgar A. Ramos, Linear-time triangulation of a simple polygon made easier via randomization, Proceedings of the sixteenth annual symposium on Computational geometry, p.201-212, June 12-14, 2000, Clear Water Bay, Kowloon, Hong Kong
[doi> 10.1145/336154.336206]
|
| |
6
|
|
| |
7
|
E. M. Arkin, M. Held, J. S. B. Mitchell, and s. S. Skiena. Hamiltonian triangulations for fast rendering. Visual Comput., 12(9): 429-444, 1996.
|
 |
8
|
|
| |
9
|
|
 |
10
|
Pankaj K. Agarwal , Micha Sharir, Pipes, cigars, and kreplach: the union of Minkowski sums in three dimensions, Proceedings of the fifteenth annual symposium on Computational geometry, p.143-153, June 13-16, 1999, Miami Beach, Florida, United States
[doi> 10.1145/304893.304960]
|
| |
11
|
P. K. Agarwal and M. Sharir. Davenport-Schinzel sequences and their geometric applications. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 1-47. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
|
| |
12
|
P. K. Agarwal and M. Sharir. Pipes, cigars, and kreplach: The union of Minkowski sums in three dimensions. Discrete Comput. Geom. 24(4): 645-685, 2000.
|
| |
13
|
P. K. Agarwal and K. R. Varadarajan. Approximating monotone polygonal curves using the uniform metric. Discrete Comput. Geom., 23, 2000. to appear.
|
| |
14
|
Marshall Bern , Erik D. Demaine , David Eppstein , Eric Kuo , Andrea Mantler , Jack Snoeyink, Ununfoldable polyhedra with convex faces, Computational Geometry: Theory and Applications, v.24 n.2, p.51-62, February 2003
[doi> 10.1016/S0925-7721(02)00091-3]
|
| |
15
|
M. Bern, D. Eppstein, P. K. Agarwal, N. Amenta, P. Chew, T. Dey, D. P. Dobkin, H. Edelsbrunner, C. Grimm, L. J. Guibas, J. Harer, J. Hass, A. Hicks, C. K. Johnson, G. Lerman, D. Letscher, P. Plassmann, E. Sedgeick, J. Snoeyink, J. Weeks, C. Yap, and D. Zorin. Emerging challenges in computational topology, 1999. Report on an NSF Workshop on computational Topology, June 11-12, Miami Beach, FL
|
| |
16
|
H. Brönnimann and M. T. Goodrich. Almost optimal set covers in finite VC-dimension. Discrete Comput. Geom., 14: 263-279, 1995.
|
| |
17
|
|
| |
18
|
M. Bern and A. Sahai. Pushing disks together — The continuous-motion case. Discrete Comput. Geom., 20: 299-514, 1998.
|
| |
19
|
J.-D. Boissonnat, M. Sharir, B. Tagansky, and M. Yvinec. Voronoi diagrams in higher dimensions under certain polyhedral distance functions. Discrete Comput. Geom., 19(4): 473-484, 1998.
|
| |
20
|
|
| |
21
|
W. S. Chan and F. Chin. Approximation of polygonal curves with minimum number of line segments or minimum error. Internat. J. Comput. Geom. Appl., 6:59-77, 1996.
|
| |
22
|
B. Chazelle. Tight bounds on the stabbing number of spanning trees in Euclidean space. Report CS-TR-155-88, Dept. Comput. Sci., Princeton Univ., Princeton, NJ, 1988.
|
| |
23
|
|
| |
24
|
T. M. Chan. Output-sensitive results on convex hulls, extreme points, and related problems. Discrete Comput. Geom., 16:369-387, 1996.
|
| |
25
|
|
| |
26
|
|
| |
27
|
|
 |
28
|
|
| |
29
|
|
| |
30
|
T. K. Dey. Improved bounds on planar k-sets and related problems. Discrete Comput. Geom., 19:373-382, 1998.
|
| |
31
|
|
 |
32
|
Matthew T. Dickerson , Scott A. McElfresh , Mark Montague, New algorithms and empirical findings on minimum weight triangulation heuristics (extended abstract), Proceedings of the eleventh annual symposium on Computational geometry, p.238-247, June 05-07, 1995, Vancouver, British Columbia, Canada
[doi> 10.1145/220279.220305]
|
| |
33
|
M. E. Dyer. Linear time algorithms for two- and three-variable linear programs. SIAM J. Comput., 13:31-45, 1984.
|
| |
34
|
|
| |
35
|
D. Eppstein. Approximating the minimum weight Steiner triangulation. Discrete Comput. Geom., 11:163-191, 1994.
|
 |
36
|
|
| |
37
|
|
| |
38
|
A. Efrat and M. Sharir. On the complexity of the union of fat objects in the plane. Discrete Comput. Geom., 23:171-189, 2000.
|
| |
39
|
|
 |
40
|
Dima Grigoriev , Marek Karpinski , Friedhelm Meyer auf der Heide , Roman Smolensky, A lower bound for randomized algebraic decision trees, Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, p.612-619, May 22-24, 1996, Philadelphia, Pennsylvania, United States
[doi> 10.1145/237814.238011]
|
| |
41
|
|
 |
42
|
|
| |
43
|
|
| |
44
|
|
| |
45
|
|
| |
46
|
L. G. Khachiyan. Polynomial algorithm in linear programming. U. S. S. R. Comput. Math. And Math. Phys., 20:53-72, 1980.
|
| |
47
|
S. Kapoor, S. N. Maheshwari, and J. S. B, Mitchell. An efficient algorithm for Euclidean shortest paths among polygonal obstacles in the plane Discrete Comput. Geom., 18:377-383, 1997.
|
| |
48
|
|
| |
49
|
|
 |
50
|
|
 |
51
|
|
| |
52
|
|
| |
53
|
J. S. B. Mitchell. Geometric shortest paths and network optimization. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 633-701. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.
|
| |
54
|
J. S. B. Mitchell, G. Rote, and G. Woeginer. Minimum-link paths among obstacles in the plane. Algorithmica, 8:431-459, 1992
|
| |
55
|
|
| |
56
|
J. Matoušek, M. Sharir, and E. Welzl. A subexponential bound for linear programming. Algorithmica, 16:498-516, 1996.
|
 |
57
|
|
| |
58
|
|
 |
59
|
|
 |
60
|
|
| |
61
|
|
| |
62
|
|
| |
63
|
|
| |
64
|
M. Sharir. Almost tight upper bounds for lower envelopes in higher dimensions. Discrete Comput. Geom. , 12:327-345, 1994.
|
| |
65
|
G. C. Shephard. Convex polytopes with convex nets. Math. Proc. Camb. Phil. Soc., 78:389-403, 1975.
|
| |
66
|
|
 |
67
|
|
 |
68
|
|
| |
69
|
J. Urrutia. Art gallery and illumination problems. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry pages 973-1027, North-Holland, 2000.
|
| |
70
|
|
| |
71
|
E. Welzl. Geometric graphs with small stabbing numbers: Combinatorics and applications. In Proc 9th Internat. Conf. Fund. Comput. Theory, Lecture Notes Comput. Sci., Springer-Verlag, 1993.
|
| |
72
|
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CITED BY 5
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Artur Czumaj , Funda Ergün , Lance Fortnow , Avner Magen , Ilan Newman , Ronitt Rubinfeld , Christian Sohler, Sublinear-time approximation of Euclidean minimum spanning tree, Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, January 12-14, 2003, Baltimore, Maryland
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