Visibility algorithms in the plane

Visibility Algorithms in the Plane

Volumn 9780521875745, Issue , 2007, Pages 1-318

  Ghosh, Subir Kumar ^a  

^a Indian Academy of Sciences   (India)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; COMPUTATIONAL GEOMETRY; COMPUTER GRAPHICS; GEOMETRY; GRAPH THEORY; STUDENTS;

GEOMETRIC GRAPHS; GEOMETRIC OBJECTS; GEOMETRIC PROPERTIES; GRADUATE STUDENTS; HIGH SPEED COMPUTERS; TIME-CONSUMING TASKS; VISIBILITY GRAPHS; WEAK VISIBILITY;

VISIBILITY;

EID: 84929743056     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511543340     Document Type: Book

References (347)

1. J. Abello, O. Egecioglu, and K. Kumar. Visibility graphs of staircase polygons and the weak Bruhat order, I: from visibility graphs to maximal chains. Discrete & Computational Geometry, 14:331-358, 1995.
2. J. Abello and K. Kumar. Visibility graphs and oriented matroids. In Proceedings of Graph Drawing, Lecture Notes in Computer Science, volume 894, pages 147-158. SpringerVerlag, Berlin, Germany, 1995.
3. J. Abello and K. Kumar. Visibility graphs and oriented matroids. Discrete & Computational Geometry, 28:449-465, 2002.
4. J. Abello, H. Lin, and S. Pisupati. On visibility graphs of simple polygons. Congressus Numerantium, 90:119-128, 1992.
5. J. Adegeest, M. H. Overmars, and J. Snoeyink. Minimum-link c-oriented path: Single source queries. International Journal of Computational Geometry and Applications, 4:39-51, 1994.
6. P. K. Agarwal. Ray shooting and other applications of spanning trees with low stabbing number. SIAM Journal on Computing, 21:540-570, 1992.
7. P. K. Agarwal, N. Alon, B. Aronov, and S. Suri. Can visibility graphs be represented compactly? Discrete & Computational Geometry, 12:347-365, 1994.
8. P. K. Agarwal and M. Sharir. Circle shooting in a simple polygon. Journal of Algorithms, 14:69-87, 1993.
9. P. K. Agarwal and M. Sharir. Circular visibility from a point in a simple polygon. International Journal of Computational Geometry and Applications, 3:1-25, 1993.
10. P.K. Agarwal, T. Biedl, S. Lazard, S. Robbins, S. Suri, and S. Whitesides. Curvature-constrained shortest paths in a convex polygon. SIAM Journal on Computing, 31:1814-1851, 2002.
11. A. Aggarwal. The art gallery theorem: its variations, applications, and algorithmic aspects. Ph.D. Thesis, Johns Hopkins University, Baltimore, MD, USA, 1984.
12. A. Aggarwal, H. Booth, J. O’Rourke, S. Suri, and C. K. Yap. Finding minimal convex nested polygons. Information and Computing, 83:98-110, 1989.
13. A. Aggarwal, S. Moran, P. Shor, and S. Suri. Computing the minimum visible vertex distance between two polygons. In Proceedings of the 1st Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science, volume 382, pages 115-134. Springer-Verlag, Berlin, Germany, 1989.
14. A. Aho, J. H. Hopcroft, and J. D. Ullman. The Design and Analysis of Algorithms. Addison-Wesley, Reading, MA, USA, 1974.
15. A. Aho, J. H. Hopcroft, and J. D. Ullman. Data Structures and Algorithms. Addison-Wesley, Reading, MA, USA, 1983.
16. L. Aleksandrov, H. Djidjev, and J. Sack. An O(n log n) algorithm for finding a shortest central link segment. International Journal of Computational Geometry and Applications, 10:157-188, 2000.
17. M. H. Alsuwaiyel and D. T. Lee. Minimal link visibility paths inside a simple polygon. Computational Geometry: Theory and Applications, 3:1-25, 1993.
18. M. H. Alsuwaiyel and D. T. Lee. Finding an approximate minimum-link visibility path inside a simple polygon. Information Processing Letters, 55:75-79, 1995.
19. N. M. Amato. Finding a closest visible vertex pair between two polygons. Algorithmica, 14:183-201, 1995.
20. T. Andreae. Some results on visibility graphs. Discrete Applied Mathematics, 40:5-18, 1992.
21. E. Arkin, M. Held, J. S. B. Mitchell, and S. Skiena. Hamiltonian triangulations for fast rendering. Visual Computers, 12:429-444, 1996.
22. E. Arkin, J. S. B. Mitchell, and C. Piatko. Minimum-link watchman tours. Information Processing Letters, 86:203-207, 2003.
23. E. Arkin, J. S. B. Mitchell, and S. Suri. Logarithmic-time link path queries in a simple polygon. International Journal of Computational Geometry and Applications, 5:369-395, 1995.
24. B. Aronov, A. Davis, T. Dey, S. P. Pal, and D. Prasad. Visibility with multiple reflections. Discrete & Computational Geometry, 20:61-78, 1998.
25. B. Aronov, A. Davis, T. Dey, S. P. Pal, and D. Prasad. Visibility with one reflection. Discrete & Computational Geometry, 19:553-574, 1998.
26. B. Aronov, L. J. Guibas, M. Teichmann, and L. Zhang. Visibility and maintenance in simple polygons. Discrete & Computational Geometry, 27:461-483, 2002.
27. T. Asano. Efficient algorithms for finding the visibility polygons for a polygonal region with holes. Transactions of IECE of Japan, E68:557-559, 1985.
28. T. Asano, T. Asano, L. J. Guibas, J. Hershberger, and H. Imai. Visibility of disjoint polygons. Algorithmica, 1:49-63, 1986.
29. T. Asano, T. Asano, and R. Pinter. Polygon triangulation: Efficiency and minimality. Journal of Algorithms, 7:221-231, 1986.
30. T. Asano, S. K. Ghosh, and T. Shermer. Visibility in the plane. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 829-876. North-Holland, Amsterdam, The Netherlands, 2000.
31. T. Asano and G. Toussaint. Computing the geodesic center of a simple polygon. In D. S. Johnson, editor, Discrete Algorithms and Complexity, Perspectives in Computing, pages 65-79. Academic Press, New York, 1987.
32. M. Atallah and D. Z. Chen. Optimal parallel algorithm for visibility of a simple polygon from a point. In Proceedings of the 5th Annual ACM Symposium on Computational Geometry, pages 114-123. ACM Press, New York, USA, 1989.
33. M. Atallah and D. Z. Chen. Parallel rectilinear shortest paths with rectangular obstacles. Computational Geometry: Theory and Applications, 1:79-113, 1991.
34. M. Atallah and D. Z. Chen. On parallel rectilinear obstacle-avoiding paths. Computational Geometry: Theory and Applications, 3:307-313, 1993.
35. M. Atallah and D. Z. Chen. Determistic parallel computational geometry. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 155-200. North-Holland, Amsterdam, The Netherlands, 2000.
36. M. Atallah, D. Z. Chen, and H. Wagener. Optimal parallel algorithm for visibility of a simple polygon from a point. Journal of the ACM, 38:516-553, 1991.
37. M. Atallah, R. Cole, and M. T. Goodrich. Cascading divide-and-conquer: A technique for designing parallel algorithms. SIAM Journal on Computing, 18:499-532, 1989.
38. M. Atallah and M. T. Goodrich. Efficient plane sweeping in parallel. In Proceedings of the 2nd Annual ACM Symposium on Computational Geometry, pages 216-225. ACM Press, New York, USA, 1986.
39. D. Avis and H. ElGindy. A combinatorial approach to polygon similarity. IEEE Transactions on Information Theory, IT-2:148-150, 1983.
40. D. Avis and D. Rappaport. Computing the largest empty convex subset of a set of points. In Proceedings of the 1st ACM Symposium on Computational Geometry, pages 161-167. ACM Press, New York, USA, 1985.
41. D. Avis and G. T. Toussaint. An efficient algorithm for decomposing a polygon into star-shaped polygons. Pattern Recognition, 13:395-398, 1981.
42. D. Avis and G. T. Toussaint. An optimal algorithm for determining the visibility of a polygon from an edge. IEEE Transactions on Computers, C-30:910-1014, 1981.
43. R. Bar-Yehuda and B. Chazelle. Triangulating disjoint Jordan chains. International Journal of Computational Geometry and Applications, 4:475-481, 1994.
44. B. Ben-Moshe, O. Hall-Holt, M. J. Katz, and J. S. B. Mitchell. Computing the visibility graph of points within a polygon. In Proceedings of the 20th Annua! ACM Symposium on Computational Geometry, pages 27-35. ACM Press, New York, USA, 2004.
45. P. Bertolazzi, S. Salza, and C. Guerra. A parallel algorithm for the visibility problem from a point. Journal of Parallel and Distributed Computing, 9:11-14, 1990.
46. J. Bhadury, V. Chandru, A. Maheshwari, and R. Chandrasekran. Art gallery problems for convex nested polygons. INFORMS Journal on Computing, 9:100-110, 1997.
47. B. K. Bhattacharya, G. Das, A. Mukhopadhyay, and G. Narasimhan. Optimally com puting a shortest weakly visible line segment inside a simple polygon. Computational Geometry: Theory and Applications, 23:1-29, 1997.
48. B. K. Bhattacharya and S. K. Ghosh. Characterizing LR-visibility polygons and related problems. Computational Geometry: Theory and Applications, 18:19-36, 2001.
49. B. K. Bhattacharya, S. K. Ghosh, and T. Shermer. A linear time algorithm to remove winding of a simple polygon. Computational Geometry: Theory and Applications, 33:165-173, 2006.
50. B. K. Bhattacharya and A. Mukhopadhyay. Computing in linear time a chord from which a simple polygon is weakly internally visible. In Proceedings of the 6th International Symposium on Algorithms and Computation, Lecture Notes in Computer Science, volume 1004, pages 22-31. Springer-Verlag, Berlin, Germany, 1995.
51. B. K. Bhattacharya, A. Mukhopadhyay, and G. Narasimhan. Optimal algorithms for two-guard walkability of simple polygons. In Proceedings of the 12th Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science, volume 2125, pages 438-449. Springer-Verlag, Berlin, Germany, 2001.
52. B. K. Bhattacharya, A. Mukhopadhyay, and G. T. Toussaint. A linear time algorithm for computing the shortest line segment from which a polygon is weakly externally visible. In Proceedings of the 2nd Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science, volume 519, pages 412-424. Springer-Verlag, Berlin, Germany, 1991.
53. B. K. Bhattacharya, A. Mukhopadhyay, and G. T. Toussaint. Computing a shortest weakly externally visible line segment for a simple polygon. International Journal of Computational Geometry and Applications, 9:81-96, 1999.
54. B. K. Bhattacharya and G. T. Toussaint. Computing shortest transversals. Computing, 46:93-119, 1991.
55. I. Bjorling-Sachs. Edge guards in rectilinear polygons. Computational Geometry: Theory and Applications, 11:111-123, 1998.
56. I. Bjorling-Sachs and D. L. Souvaine. An efficient algorithm for guard placement in polygons with holes. Discrete & Computational Geometry, 13:77-109, 1995.
57. J.-D. Boissonnat, S. K. Ghosh, T. Kavitha, and S. Lazard. An algorithm for computing a convex path of bounded curvature in a simple polygon. Algorithmica, 34:109-156, 2002.
58. J. A. Bondy and U. S. R. Murty. Graph Theory with Applications. North Holland, New York, USA, 1985.
59. K. S. Booth and G. S. Lueker. Testing for consecutive ones property, interval graphs and graph planarity using pq-tree algorithms. Journal of Computer and Systems Sciences, 13:335-379, 1976.
60. P. Bose, A. Lubiw, and J. Munro. Efficient visibility queries in simple polygons. Computational Geometry: Theory and Applications, 23:313-335, 2002.
61. A. Brandstadt, J. Spinrad, and L. Stewart. Bipartite permutation graphs are bipartite tolerance graphs. Congressus Numerantium, 58:165-174, 1987.
62. M. Breen. Clear visibility and the dimension of kernels of starshaped sets. Proceedings of the American Mathematical Society, 85:414-418, 1982.
63. M. Breen. Clear visibility and unions of two starshaped sets in the plane. Pacific Journal of Mathematics, 115:267-275, 1984.
64. D. Bremner. Point Visibility Graphs and Restricted-Orientation Polygon Covering. M.Sc. Thesis, School of Computing Science, Simon Fraser University, Burnaby, BC, Canada, 1993.
65. D. Bremner and T. Shermer. Point visibility graphs and o-convex cover. International Journal of Computational Geometry and Applications, 10:55-71, 2000.
66. A. Briggs and B. Donald. Visibility-based planning of sensor control strategies. Algorithmica, 26:364-388, 2000.
67. H. Brunn. Uber kerneigebiete. Mathematische Annalen, 73:436-440, 1913.
68. M. Buckinghan. Circle graphs. Ph.D. Dissertation, Courant Institute of Mathematical Sciences, New York, USA, 1980.
69. V. Chandru, S. K. Ghosh, A. Maheshwari, V. T. Rajan, and S. Saluja. NC-algorithms for minimum link path and related problems. Journal of Algorithms, 19:173-203, 1995.
70. B. Chazelle. A theorem on polygon cutting with applications. In Proceedings of the 23rd IEEE Symposium on the Foundations of Computer Science, pages 339-349. IEEE Computer Society Press, Los Alamitos, CA, USA, 1982.
71. B. Chazelle. Triangulating a simple polygon in linear time. Discrete & Computational Geometry, 6:485-524, 1991.
72. B. Chazelle and H. Edelsbrunner. An optimal algorithm for intersecting line segments in the plane. Journal of the ACM, 39:1-54, 1992.
73. B. Chazelle, H. Edelsbrunner, M. Grigni, L. J. Guibas, J. Hershberger, M. Sharir, and J. Snoeyink. Ray shooting in polygons using geodesic triangulations. Algorithmica, 12:54-68, 1994.
74. B. Chazelle and L. J. Guibas. Fractional cascading: I. A data structuring technique. Algorithmica, 1:133-162, 1986.
75. B. Chazelle and L. J. Guibas. Fractional cascading: II. Applications. Algorithmica, 1:163-191, 1986.
76. B. Chazelle and L. J. Guibas. Visibility and intersection problems in plane geometry. Discrete & Computational Geometry, 4:551-581, 1989.
77. B. Chazelle, L. J. Guibas, and D.T. Lee. The power of geometric duality. BIT, 25:76-90, 1985.
78. B. Chazelle and J. Incerpi. Triangulation and shape-complexity. ACM Transactions of Graphics, 3:135-152, 1984.
79. O. Chein and L. Steinberg. Routing past unions of disjoint barriers. Networks, 13:389 398, 1983.
80. D. Chen, K. Klenk, and H.-Y. Tu. Shortest path queries among weighted obstacles in the rectilinear plane. SIAM Journal on Computing, 29:1223-1246, 2000.
81. D. Z. Chen. Efficient geometric algorithms on EREW-PRAM. IEEE Transactions on Parallel and Distributed Systems, 6:41-47, 1995.
82. D. Z. Chen. An optimal parallel algorithm for detecting weak visibility of a simple polygon. International Journal of Computational Geometry and Applications, 5:93-124, 1995.
83. D. Z. Chen. Optimally computing the shortest weakly visible subedge of a simple polygon. Journal of Algorithms, 20:459-478, 1996.
84. D. Z. Chen. Determining weak visibility of a polygon from an edge in parallel. International Journal of Computational Geometry and Applications, 8:277-304, 1998.
85. D. Z. Chen, O. Daescu, and K. Klenk. On geometric path query problems. International Journal of Computational Geometry and Applications, 11:617-645, 2001.
86. Y.-J. Chiang and J. S. B. Mitchell. Two-point Euclidean shortest path queries in the plane. In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 215-224. ACM and SIAM, USA, 1999.
87. Y.-J. Chiang and R. Tamassia. Optimal shortest path and minimum-link path queries between two convex polygons inside a simple polygonal obstacle. International Journal of Computational Geometry and Applications, 7:85-121, 1997.
88. F. Chin, J. Sampson, and C. A. Wang. A unifying approach for a class of problems in the computational geometry of polygons. The Visual Computer, 1:124-132, 1985.
89. S.-H. Choi, S. Y. Shin, and K.-Y. Chwa. Characterizing and recognizing the visibility graph of a funnel-shaped polygon. Algorithmica, 14:27-51, 1995.
90. S.-Y. Chou and R. C. Woo. A linear-time algorithm for constructing a circular visibility diagram. Algorithmica, 14:203-228, 1995.
91. V. Chvátal. A combinatorial theorem in plane geometry. Journal of Combinatorial Theory, Series B, 18:39-41, 1975.
92. K. L. Clarkson, S. Kapoor, and P. Vaidya. Rectilinear shortest paths through polygonal obstacles in O(nlog n) time. In Proceedings of the 3rd Annual ACM Symposium on Computational Geometry, pages 251-257. ACM Press, New York, USA, 1987.
93. M. Cohen and J. Wallace. Radiosity and Realistic Image Synthesis. Academic Press Professional, Boston, MA, USA, 1993.
94. R. Cole. Searching and storing similar lists. Journal of Algorithms, 7:202-220, 1986.
95. P. Colley, A. Lubiw, and J. Spinrad. Visibility graphs of towers. Computational Geometry: Theory and Applications, 7:161-172, 1997.
96. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms. MIT Press, Cambridge, MA, USA, 2001.
97. C. Coullard and A. Lubiw. Distance visibility graphs. International Journal of Computational Geometry and Applications, 2:349-362, 1992.
98. D. Crass, I. Suzuki, and M. Yamashita. Search for a mobile intruder in a corridor-the open edge variant of the polygon search propblem. International Journal of Computational Geometry and Applications, 5:397-412, 1995.
99. J. Culberson and R. Reckhow. Orthogonally convex coverings of orthogonal polygons without holes. Journal of Computer and Systems Science, 39:166-204, 1989.
100. G. Das, P. Heffernan, and G. Narasimhan. Finding all weakly-visible chords of a polygon in linear time. Nordic Journal of Computing, 1:433-456, 1994.
101. G. Das, P. Heffernan, and G. Narasimhan. LR-visibility in polygons. Computational Geometry: Theory and Applications, 7:37-57, 1997.
102. G. Das and G. Narasimhan. Geometric searching and link distance. In Proceedings of the 2nd Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science, volume 519, pages 262-272. Springer-Verlag, Berlin, Germany, 1991.
103. G. Das and G. Narasimhan. Optimal linear-time algorithm for the shortest illuminating line segment in a polygon. In Proceedings of the 10th Annua! ACM Symposium on Computational Geometry, pages 259-266. ACM Press, New York, USA, 1994.
104. D. Dasgupta and C.E. Veni Madhavan. An approximate algorithm for the minimum vertex nested polygon problem. Information Processing Letters, 33:35-44, 1989.
105. P. Dasgupta, P. Chakrabarti, and S. De Sarkar. A new competitive algorithm for agent searching in unknown streets. In Proceeding of the 16th Symposium on Foundation of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science, volume 1180, pages 32-41. Springer-Verlag, Berlin, Germany, 1995.
106. A. Datta and C. Icking. Competitive searching in a generalized street. Computational Geometry: Theory and Applications, 13:109-120, 1997.
107. L. Davis and M. Benedikt. Computational models of space: Isovists and isovist fields. Computer Graphics and Image Processing, 11:49-72, 1979.
108. M. de Berg. On rectilinear link distance. Computational Geometry: Theory and Applications, 1:13-34, 1991.
109. P. de Rezende, D. T. Lee, and Y. F. Wu. Rectilinear shortest paths with rectangular barriers. Discrete & Computational Geometry, 4:41-53, 1989.
110. J. Dean, A. Lingas, and J.-R. Sack. Recognizing polygons, or how to spy. The Visual Computer, 3:344-355, 1988.
111. H. N. Djidjev, A. Lingas, and J. Sack. An O(n log n) algorithm for computing the link center of a simple polygon. Discrete & Computational Geometry, 8:131-152, 1992.
112. D. Dobkin and R. Lipton. Multidimensional searching problems. SIAM Journal on Computing, 5:181-186, 1975.
113. D. Dobkin and S. Teller. Computer graphics. In J. Goodman and J. O’Rourke, editors, Handbook of Discrete and Computational Geometry, pages 779-814. CRC Press, New York, USA, 1997.
114. J.-I. Doh and K.-Y. Chwa. An algorithm for determining visibility of a simple polygon from an internal line segment. Journal of Algorithms, 14:139-168, 1993.
115. S. E. Dorward. A survey of object-space hidden surface removal. International Journal of Computational Geometry and Applications, 4:325-362, 1994.
116. H. Edelsbrunner. Finding extreme distance between convex polygons. Journal of Algorithms, 6:213-224, 1985.
117. H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, Berlin, Germany, 1987.
118. H. Edelsbrunner, L. J. Guibas, and M. Sharir. The complexity and construction of many faces in arrangements of lines and segments. Discrete & Computational Geometry, 5:161-196, 1990.
119. H. Edelsbrunner, L. J. Guibas, and J. Stolfi. Optimal point location in a monotone subdivision. SIAM Journal on Computing, 15:317-340, 1986.
120. H. Edelsbrunner, J. O’Rourke, and R. Seidel. Constructing arrangements of lines and hyperplanes with applications. SIAM Journal on Computing, 15:341-363, 1986.
121. H. Edelsbrunner, J. O’Rourke, and E. Welzl. Stationing guards in rectilinear art galleries. Computer Vision, Graphics, Image Processing, 27:167-176, 1984.
122. A. Efrat and S. Har-Peled. Guarding galleries and terrains. In Proceedings of the 2nd IFIP International Conference on Theoretical Computer Science, pages 181-192. Kluwer Academic Publishers, Norwell, MA, USA, 2002.
123. S. Eidenbenz. Inapproximability results for guarding polygons without holes. In Proceedings of International Symposium on Algorithms and Computations, Lecture Notes in Computer Science, volume 1533, pages 427-436. Springer-Verlag, Berlin, Germany, 1998.
124. S. Eidenbenz. In-approximability of visibility problems on polygons and terrains. Ph.D. Thesis, Institute for Theoretical Computer Science, ETH, Zurich, Switzerland, 2000.
125. S. Eidenbenz. In-approximability of finding maximum hidden sets on polygons and terrains. Computational Geometry: Theory and Applications, 21:139-153, 2002.
126. H. ElGindy. Hierarchical decomposition of polygons with applications. Ph.D. Thesis, McGill University, Montreal, Quebec, Canada, 1985.
127. H. ElGindy. Efficient algorithms for computing the weak visibility polygon from an edge. Technical Report MS-CIS-86-04, University of Pennsylvania, Philadelphia, USA, 1986.
128. H. ElGindy and D. Avis. A linear algorithm for computing the visibility polygon from a point. Journal of Algorithms, 2:186-197, 1981.
129. H. ElGindy and M. Goodrich. Parallel algorithms for shortest path problems in polygons. Visual Computer, 3:371-378, 1988.
130. H. ElGindy and P. Mitra. Orthogonal shortest route queries among axis parallel rectangular obstacles. International Journal of Computational Geometry and Applications,4:3-24, 1994.
131. H. ElGindy and G. T. Toussaint. On geodesic properties of polygons relevant to linear time triangulation. The Visual Computer, 5:68-74, 1989.
132. S. Even, A. Pnueli, and A. Lempel. Permutation graphs and transitive graphs. Journal of the ACM, 19:400-410, 1972.
133. H. Everett. Visibility graph recognition. Ph.D. Thesis, University of Toronto, Toronto, Canada, 1990.
134. H. Everett and D. G. Corneil. Recognizing visibility graphs of spiral polygons. Journal of Algorithms, 11:1-26, 1990.
135. H. Everett and D. G. Corneil. Negative results on characterizing visibility graphs. Computational Geometry: Theory and Applications, 5:51-63, 1995.
136. H. Everett, C. T. Hoang, K. Kilakos, and M. Noy. Planar segment visibility graphs. Computational Geometry: Theory and Applications, 16:235-243, 2000.
137. H. Everett, F. Hurtado, and M. Noy. Stabbing information of a simple polygon. Discrete Applied Mathematics, 91:67-92, 1999.
138. H. Everett, A. Lubiw, and J. O’Rourke. Recovery of convex hulls from external visibility graphs. In Proceedings of the 5th Canadian Conference on Computational Geometry, pages 309-314, 1993.
139. O. Faugeras. Three Dimensional Computer Vision. MIT Press, Cambridge, MA, USA, 1993.
140. E. Fink and D. Wood. Planar strong visibility. International Journal of Computational Geometry and Applications, 13:173-187, 2003.
141. S. Fisk. A short proof of Chvatal's watchman theorem. Journal of Combinatorial Theory, Series B, 24:374, 1978.
142. A. Fournier and D. Y. Montuno. Triangulating simple polygons and equivalent problems. ACM Transactions of Graphics, 3:153-174, 1984.
143. M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34:596-615, 1987.
144. D. R. Fulkerson and O. A. Gross. Incident matrics and interval graphs. Pacific Journal of Mathematics, 15:835-855, 1965.
145. C. P. Gabor, W. Hsu, and K. J. Supowit. Recognizing circle graphs in polynomial time. Journal of the ACM, 36:435-473, 1989.
146. H. N. Gabow and R. E. Tarjan. A linear-time algorithm for a special case of disjoint set union. Journal of Computer Systems and Science, 30:209-221, 1985.
147. J. Garcia-Lopez and P. Ramos-Alonso. Circular visibility and separability. In Proceedings of the 5th Canadian Conference on Computational Geometry, pages 18-23, 1993.
148. M. R. Garey, D. S. Johnson, F. P. Preparata, and R. E. Tarjan. Triangulating a simple polygon. Information Processing Letters, 7:175-179, 1978.
149. L. Gewali. Efficient algorithms for path planning and visibility problems. Ph.D. Thesis, University of Texas, Dallas, Texas, USA, 1989.
150. L. Gewali, M. Keil, and S. Ntafos. On covering orthogonal polygons with star-shaped polygons. Information Sciences, 65:45-63, 1992.
151. S. K. Ghosh. A linear time algorithm for determining the intersection type of two star polygons. In Proceedings of the 4th Symposium on Foundation of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science, volume 181, pages 317-330. Springer Verlag, Berlin, Germany, 1984.
152. S. K. Ghosh. Approximation algorithms for art gallery problems. In Proceedings of the Canadian Information Processing Society Congress, pages 429-434, 1987.
153. S. K. Ghosh. Computing a viewpoint of a set of points inside a polygon. In Proceedings of the 8th Symposium on Foundation of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science, volume 338, pages 18-29. Springer Verlag, Berlin, Germany, 1988.
154. S. K. Ghosh. On recognizing and characterizing visibility graphs of simple polygons. In Proceedings of Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, volume 318, pages 96-104. Springer-Verlag, Berlin, Germany, 1988. (Also In Report JHU/EECS-86/14, The Johns Hopkins University, Baltimore, MD, USA, 1986).
155. S. K. Ghosh. Computing visibility polygon from a convex set and related problems. Journal of Algorithms, 12:75-95, 1991.
156. S. K. Ghosh. A note on computing the visibility polygon from a convex chain. Journal of Algorithms, 21:657-662, 1996.
157. S. K. Ghosh. On recognizing and characterizing visibility graphs of simple polygons. Discrete & Computational Geometry, 17:143-162, 1997.
158. S. K. Ghosh. Approximation algorithms for art gallery problems in polygons. Manuscript, Tata Institute of Fundamental Research, Mumbai, India, January 2006.
159. S. K. Ghosh and A. Maheshwari. An optimal algorithm for computing a minimum nested nonconvex polygon. Information Processing Letters, 36:277-280, 1990.
160. S. K. Ghosh and A. Maheshwari. An optimal parallel algorithm for determining the intersection type of two star-shaped polygons. In Proceedings of the 3rd Canadian Conference on Computational Geometry, pages 2-6, 1991.
161. S. K. Ghosh and A. Maheshwari. Parallel algorithms for all minimum link paths and link center problems. In Proceedings of the 3rd Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, volume 621, pages 106- 117. SpringerVerlag, Berlin, Germany, 1992.
162. S. K. Ghosh, A. Maheshwari, S. P. Pal, S. Saluja, and C. E. Veni Madhavan. Computing the shortest path tree in a weak visibility polygon. In Proceedings of the 11th Symposium on Foundation of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science, volume 560, pages 369-389. Springer-Verlag, Berlin, Germany, 1991.
163. S. K. Ghosh, A. Maheshwari, S. P. Pal, S. Saluja, and C. E. Veni Madhavan. Characterizing and recognizing weak visibility polygons. Computational Geometry: Theory and Applications, 3:213-233, 1993.
164. S. K. Ghosh, A. Maheshwari, S. P. Pal, and C. E. Veni Madhavan. An algorithm for recognizing palm polygons. The Visual Computer, 10:443-451, 1994.
165. S. K. Ghosh and D. M. Mount. An output-sensitive algorithm for computing visibility graphs. SIAM Journal on Computing, 20:888-910, 1991.
166. S. K. Ghosh and S. Saluja. Optimal on-line algorithms for walking with minimum number of turns in unknown streets. Computational Geometry: Theory and Applications, 8:241-266, 1997.
167. S. K. Ghosh, T. Shermer, B. K. Bhattacharya, and P. Goswami. Computing the maximum clique in the visibility graph of a simple polygon. Journal of Discrete Algorithms, to appear, 2007.
168. Z. Gigus, J. Canny, and R. Seidel. Efficiently computing and representing aspect graphs of polyhedral objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13:542-551, 1991.
169. P. C. Gilmore and A. J. Hoffman. A characterization of comparability graphs and of interval graphs. Canadian Journal of Mathematics, 16:539-548, 1964.
170. M.C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, USA, 1980.
171. M. T. Goodrich. Triangulating a polygon in parallel. Journal of Algorithms, 10:327-351, 1989.
172. M. T. Goodrich. Parallel algorithms in geometry. In J. Goodman and J. O’Rourke, editors, Handbook of Discrete and Computational Geometry, pages 953-967. CRC Press, New York, USA, 1997.
173. M. T. Goodrich, S. Shauck, and S. Guha. Parallel methods for visibility and shortestpath problems in simple polygons. Algorithmica, 8:461-486, 1992.
174. M. T. Goodrich, S. Shauck, and S. Guha. Addendum to ‘parallel methods for visibility and shortest path problems in simple polygons’. Algorithmica, 9:515-516, 1993.
175. R. L. Graham and F. F. Yao. Finding the convex hull of a simple polygon. Journal of Algorithms, 4:324-331, 1983.
176. P. M. Gruber and J. M. Wills, editors. Handbook of Convex Geometry. North-Holland, Amsterdam, The Netherlands, 1993.
177. L. J. Guibas and J. Hershberger. Optimal shortest path queries in a simple polygon. Journal of Computer and System Science, 39:126-152, 1989.
178. L. J. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. E. Tarjan. Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica, 2:209-233, 1987.
179. L. J. Guibas, J. Hershberger, J. S. B. Mitchell, and J. Snoeyink. Approximating polygons and subdivisions with minimum-link paths. International Journal of Computational Geometry and Applications, 3:383-415, 1993.
180. L. J. Guibas, J. C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. International Journal of Computational Geometry and Applications, 9:471-494, 1999.
181. L. J. Guibas, R. Motwani, and P. Raghavan. The robot localization problem. SIAM Journal on Computing, 26:1120-1138, 1997.
182. Györi, F. Hoffmann, K. Kriegel, and T. Shermer. Generalized guarding and partitioning for rectilinear polygons. Computational Geometry: Theory and Applications, 6:21-44, 1996.
183. P. J. Heffernan. Linear-time algorithms for weakly-monotone polygons. Computational Geometry: Theory and Applications, 3:121-137, 1993.
184. P. J. Heffernan. An optimal algorithm for the two-guard problems. International Journal of Computational Geometry and Applications, 6:15-44, 1996.
185. P. J. Heffernan and J. S. B. Mitchell. An optimal algorithm for computing visibility in the plane. SIAM Journal on Computing, 24:184-201, 1995.
186. J. Hershberger. Finding the visibility graph of a polygon in time proportional to its size. Algorithmica, 4:141-155, 1989.
187. J. Hershberger. Optimal parallel algorithms for triangulated simple polygons. International Journal of Computational Geometry and Applications, 5:145-170, 1995.
188. J. Hershberger and J. Snoeyink. Computing minimum link paths of a given homotopy class. Computational Geometry: Theory and Applications, 4:63-97, 1994.
189. J. Hershberger and S. Suri. Efficient computation of Euclidean shortest paths in the plane. In Proceedings of the 34th IEEE Symposium on the Foundations of Computer Science, pages 508-517. IEEE Computer Society Press, Los Alamitos, CA, USA, 1993.
190. J. Hershberger and S. Suri. A pedestrain approach to ray shooting: shoot a ray, take a walk. Journal of Algorithms, 18:403-413, 1995.
191. J. Hershberger and S. Suri. Matrix searching with the shortest path metric. SIAM Journal on Computing, 26:1612-1634, 1997.
192. J. Hershberger and S. Suri. An optimal-time algorithm for Euclidean shortest paths in the plane. SIAM Journal on Computing, 28:2215-2256, 1999.
193. S. Hertel and K. Mehlhorn. Fast triangulation of the plane with respect to simple polygons. Information and Control, 64:52-76, 1985.
194. F. Hoffmann, M. Kaufmann, and K. Kriegel. The art gallery theorem for polygons with holes. In Proceedings of the 32nd IEEE Symposium on the Foundation of Computer Science, pages 39-48. IEEE Computer Society Press, Los Alamitos, CA, USA, 1991.
195. K. Hoffmann, K. Mehlhorn, P. Rosenstiehl, and R. E. Tarjan. Sorting Jordan sequences in linear time using level-linked search trees. Information and Control, 68:170-184, 1986.
196. M. Hoffmann and C. Toth. Alternating paths through disjoint line segments. Information Processing Letters, 87:287-294, 2003.
197. M. Hoffmann and C. Toth. Segment endpoint visibility graphs are hamiltonian. Computational Geometry: Theory and Applications, 26:47-68, 2003.
198. R. Honsberger. Mathematical Gems II. Mathematical Associations for America, New York, USA, 1979.
199. F. R. Hsu, R. C. Chang, and R. C. T. Lee. Parallel algorithms for computing the closest visible vertex pair between two polygons. International Journal of Computational Geometry and Applications, 2:135-162, 1992.
200. C. Icking and R. Klein. The two guards problem. International Journal of Computational Geometry and Applications, 2:257-285, 1992.
201. C. Icking and R. Klein. Searching for the kernel of a polygon: A competitive strategy. In Proceedings of the 11th Annual ACM Symposium on Computational Geometry, pages 258-266. ACM Press, New York, USA, 1995.
202. C. Icking, R. Klein, E. Langetepe, S. Schuierer, and I. Semrau. An optimal competitive strategy for walking in streets. SIAM Journal on Computing, 33:462-486, 2004.
203. L. Jackson and S. K. Wismath. Orthogonal polygon reconstruction from stabbing information. Computational Geometry: Theory and Applications, 23:69-83, 2002.
204. B. Joe. On the correctness of a linear-time visibility polygon algorithm. International Journal of Computer Mathematics, 32:155-172, 1990.
205. B. Joe and R. B. Simpson. Corrections to Lee's visibility polygon algorithm. BIT, 27:458-473, 1987.
206. S. Kahan and J. Snoeyink. On the bit complexity of minimum link paths: superquadratic algorithms for problems solvable in linear time. In Proceedings of the 12th Annual ACM Symposium on Computational Geometry, pages 151-158. ACM Press, New York, USA, 1996.
207. J. Kahn, M. Klawe, and D. Kleitman. Traditional galleries require fewer watchmen. SIAM Journal of Algebraic and Discrete Methods, 4:194-206, 1983.
208. G. Kant. A more compact visibility representation. International Journal of Computational Geometry and Applications, 7:197-210, 1997.
209. S. Kapoor and S. N. Maheshwari. Efficiently constructing the visibility graph of a simple polygon with obstacles. SIAM Journal on Computing, 30:847-871, 2000.
210. S. Kapoor, S. N. Maheshwari, and J. S. B. Mitchell. An efficient algorithm for Euclidian shortest paths among polygonal obstacles in the plane. Discrete & Computational Geometry, 18:377-383, 1997.
211. R. M. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, volume 1, pages 869-941. Elsevier/The MIT Press, Cambridge, MA, USA, 1990.
212. Y. Ke. An efficient algorithm for link distance problems inside a simple polygon. Technical Report Report JHU-87/28, Department of Computer Science, The Johns Hopkins University, Baltimore, MD, USA, 1988.
213. M. Keil. Finding a hamiltonian circits in interval graphs. Information Processing Letters, 20:201-206, 1985.
214. M. Keil. Minimally covering a horizontally convex polygon. In Proceedings of the 2nd, Annual ACM Symposium on Computational Geometry, pages 43-51. ACM Press, New York, USA, 1986.
215. S.-H. Kim, S. Y. Shin, and K.-Y. Chwa. Efficient algorithms for solving diagonal visibility problems in a simple polygon. International Journal of Computational Geometry and Applications, 5:433-458, 1995.
216. D. Kirkpatrick. Optimal search in planar subdivision. SIAM Journal on Computing, 12:28-35, 1983.
217. D. Kirkpatrick, M. Klawe, and R. E. Tarjan. Polygon triangulation in O(n log log n) time with simple data structures. Discrete & Computational Geometry, 7:329-346, 1992.
218. D. Kirkpatrick and S. Wismath. Determining bar-representability for ordered weighted graphs. Computational Geometry: Theory and Applications, 6:99-122, 1996.
219. R. Klein. Walking an unknown street with bounded detour. Computational Geometry: Theory and Applications, 1:325-351, 1992.
220. J. Kleinberg. On-line search in a simple polygon. In Proceedings of the 5th ACM-SIAM Symposium on Discrete Algorithms, pages 8-15. ACM and SIAM, USA, 1994.
221. D. Kozen. The Design and Analysis of Algorithms. Springer-Verlag, New York, USA, 1992.
222. E. Kranakis, D. Krizanc, and L. Meertens. Link length of rectilinear Hamiltonian tours in grids. Ars Combinatoria, 38:177-192, 1994.
223. M. A. Krasnosel'skii. Sur un critere pour qu’un domaine soit etoile. Matematicheskij Sbornik, 19:309-310, 1946.
224. C. Kuratowski. Sur le probléme des courbes gauches en topologie. Fundamental Mathematics, 15:271-283, 1930.
225. R. Larson and V. Li. Finding minimum rectilinear distance paths in the presence of barriers. Networks, 11:285-304, 1981.
226. J. C. Latombe. Robot Motion Planning. Kluwer Academic Publishers, Boston, MA, USA, 1991.
227. S. M. LaValle. Planning Algorithms. Cambridge University Press, New York, USA, 2006.
228. S. M. LaValle, B. Simov, and G. Slutzki. An algorithm for searching a polygonal region with a flashlight. International Journal of Computational Geometry and Applications, 12:87-113, 2002.
229. D. T. Lee. Proximity and reachability in the plane. Ph.D. Thesis, Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, IL, USA, 1978.
230. D. T. Lee. Visibility of a simple polygon. Computer Vision, Graphics, and Image Processing, 22:207-221, 1983.
231. D. T. Lee and A. K. Lin. Computational complexity of art gallery problems. IEEE Transactions on Information Theory, IT-32:276-282, 1986.
232. D. T. Lee and A. K. Lin. Computing the visibility polygon from an edge. Computer Vision, Graphics, and Image Processing, 34:1-19, 1986.
233. D. T. Lee and F. P. Preparata. Location of a point in a planar subdivision and its applications. SIAM Journal on Computing, 6:594-606, 1977.
234. D. T. Lee and F. P. Preparata. An optimal algorithm for finding the kernel of a polygon. Journal of the ACM, 26:415-421, 1979.
235. D. T. Lee and F. P. Preparata. Euclidean shortest paths in the presence of rectilinear barriers. Networks, 14:393-415, 1984.
236. J. Lee, S. Park, and K. Chwa. Searching a polygonal room with one door by a 1-searcher. International Journal of Computational Geometry and Applications, 10:201-220, 2000.
237. J. Lee, S. Park, and K. Chwa. Simple algorithms for searching a polygon with flashlights. Information Processing Letters, 81:265-270, 2002.
238. J. Lee, C. Shin, J. Kim, S. Shin, and K. Chwa. New competitive strategies for searching in unknown star-shaped polygons. In Proceedings of the 13th Annua! ACM Symposium on Computational Geometry, pages 427-429. ACM Press, New York, USA, 1997.
239. S. H. Lee and K.-Y. Chwa. A new triangulation-linear class of simple polygons. International Journal of Computer Mathematics, 22:135-147, 1987.
240. C. G. Lekkerkerker and J. Ch. Representation of a finite graphs by a set of intervals on the real line. Fundamental Mathematics, 51:45-64, 1962.
241. W. Lenhart, R. Pollack, J.-R. Sack, R. Seidel, M. Sharir, S. Suri, G. T. Toussaint, S. Whitesides, and C. K. Yap. Computing the link center of a simple polygon. Discrete & Computational Geometry, 3:281-293, 1988.
242. N. J. Lennes. Theorems on the simple finite polygon and polyhedron. American Journal of Mathematics, 33:37-62, 1911.
243. S. Y. Lin and C. Y. Chen. Planar visibility graphs. In Proceedings of the 6th Canadian Conference on Computational Geometry, pages 30-35, 1994.
244. S. Y. Lin and S. Skiena. Complexity aspects of visibility graphs. International Journal of Computational Geometry and Applications, 5:289-312, 1995.
245. A. Lingas, A. Maheshwari, and J.-R. Sack. Optimal parallel algorithms for rectilinear link-distance problems. Algorithmica, 14:261-289, 1995.
246. A. Lopez-Ortiz. On-line target searching in bounded, and unbounded, domains. Ph.D. Thesis, University of Waterloo, Waterloo, Ont., Canada, 1996.
247. A. Lopez-Ortiz and S. Schuierer. Lower bounds for streets and generalized streets. International Journal of Computational Geometry and Applications, 11:401-421, 2001.
248. A. Lopez-Ortiz and S. Schuierer. Searching and on-line recognition of star-shaped polygons. Information and Computation, 185:66-88, 2003.
249. T. Lozano-Perez and M. A. Wesley. An algorithm for planning collision-free paths among polyhedral obstacles. Communications of ACM, 22:560-570, 1979.
250. A. Lubiw. Decomposing polygons into convex quadrilaterals. In Proceedings of the 1st ACM Symposium on Computational Geometry, pages 97-106. ACM Press, New York, USA, 1985.
251. G. MacDonald and T. Shermer. Isomorphism of spiral polygons. Discrete & Computational Geometry, 16:277-304, 1996.
252. A. Maheshwari and J.-R. Sack. Simple optimal algorithms for rectilinear link path and polygon separation problems. Parallel Processing Letters, 9:31-42, 1999.
253. A. Maheshwari, J.-R. Sack, and H. Djidjev. Link distance problems. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 519-558. North- Holland, Amsterdam, The Netherlands, 2000.
254. K. McDonald and J. Peters. Smallest paths in simple rectilinear polygons. IEEE Transactions on Computer Aided Design, 11:264-273, 1992.
255. M. McKenna and G. T. Toussaint. Finding the minimum vertex distance between two disjoint convex polygons in linear time. Computers and Mathematics with Applications, 11:1227-1242, 1985.
256. K. Mehlhorn. Data Structures and Algorithms, Volume 1: Sorting and searching. Springer-Verlag, Berlin, Germany, 1984.
257. K. Mehlhorn. Data Structures and Algorithms, Volume 3: Multi-Dimensional Searching and Computational Geometry. Springer-Verlag, Berlin, Germany, 1984.
258. 1 shortest paths among obstacles in the plane. Algorithmica, 8:55-88, 1992.
259. J. S. B. Mitchell. Shortest paths among obstacles in the plane. International Journal of Computational Geometry and Applications, 6:309-332, 1996.
260. 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. North-Holland, Amsterdam, The Netherlands, 2000.
261. J. S. B. Mitchell, C. Piatko, and E. Arkin. Computing a shortest k-link path in a polygon. In Proceedings of the 33rd IEEE Symposium on the Foundations of Computer Science, pages 573-582. IEEE Computer Society Press, Los Alamitos, CA, USA, 1992.
262. J. S. B. Mitchell, G. Rote, and G. Woeginger. Minimum-link paths among obstacles in the plane. Algorithmica, 8:431-459, 1992.
263. R. Motwani, A. Raghunathan, and H. Saran. Perfect graphs and orthogonally convex covers. SIAM Journal on Discrete Mathematics, 2:431-459, 1989.
264. R. Motwani, A. Raghunathan, and H. Saran. Covering orthogonal polygons with star polygons: the perfect graph approach. Journal of Computer and Systems Science, 40:19-48, 1990.
265. J. I. Munro, M. H. Overmars, and D. Wood. Variations on visibility. In Proceedings of the 3rd Annual ACM Symposium on Computational Geometry, pages 291-299. ACM Press, New York, USA, 1987.
266. G. Narasimhan. On hamiltonian triangulations of simple polygons. International Journal of Computational Geometry and Applications, 9:261-275, 1999.
267. B. J. Nilsson and S. Schuierer. Computing the rectilinear link diameter of a polygon. In Proceedings of International Workshop on Computational Geometry 1991, Computational Geometry-Methods, Algorithms and Applications, Lecture Notes in Computer Science, volume 553, pages 203-215. Springer-Verlag, Berlin, Germany, 1991.
268. B. J. Nilsson and S. Schuierer. An optimal algorithm for the rectilinear link center of a rectilinear polygon. Computational Geometry: Theory and Applications, 6:169-194, 1996.
269. J. O’Rourke. An alternative proof of the rectilinear art gallery theorem. Journal of Geometry, 211:118-130, 1983.
270. J. O’Rourke. Galleries need fewer mobile guards: A variation on Chvatal's theorem. Geometricae Dedicata, 4:273-283, 1983.
271. J. O’Rourke. Art Gallery Theorems and Algorithms. Oxford University Press, New York, USA, 1987.
272. J. O’Rourke. Computational Geometry in C. Cambridge University Press, New York, USA, 1998.
273. J. O’Rourke and J. Rippel. Two segment classes with Hamiltonian visibility graphs. Computational Geometry: Theory and Applications, 4:209-218, 1994.
274. J. O’Rourke and I. Streinu. Vertex-edge pseudo-visibility graphs: characterization and recognition. In Proceedings of the 13th Annual ACM Symposium on Computational Geometry, pages 119-128. ACM Press, New York, USA, 1997.
275. J. O’Rourke and I. Streinu. The vertex edge visibility graph of a polygon. Computational Geometry: Theory and Applications, 10:105-120, 1998.
276. J. O’Rourke and K. Supowit. Some NP-hard polygon decomposition problems. IEEE Transactions on Information Theory, IT-29:181-190, 1983.
277. M. H. Overmars and J. V. Leeuwen. Maintenance of configurations in the plane. Journal of Computer and Systems Sciences, 23:166-204, 1981.
278. M. H. Overmars and E. Welzl. New methods for computing visibility graphs. In Proceedings of the 4th Annual ACM Symposium on Computational Geometry, pages 164-171. ACM Press, New York, USA, 1988.
279. M. H. Overmars and D. Wood. On rectangular visibility. Journal of Algorithms, 9:372-390, 1988.
280. S. P. Pal. Weak visibility and related problems on simple polygons. Ph.D. Thesis, Indian Institute of Science, Bangalore, India, September 1990.
281. S. P. Pal, S. Brahma, and D. Sarkar. A linear worst-case lower bound on the number of holes in regions visible due to multiple diffuse reflections. Journal of Geometry, 81:5-14, 2004.
282. S. Park, J. Lee, and K. Chwa. Searching a room by two guards. International Journal of Computational Geometry and Applications, 12:339-352, 2002.
283. M. A. Peshkin and A. C. Sanderson. Reachable grasps on a polygon: the convex rope algorithm. IEEE Journal on Robotics and Automation, RA-2:53-58, 1986.
284. A. Pnueli, A. Lempel, and S. Even. Transitive orientation of graphs and identification of permutation graphs. Canadian Journal of Mathematics, 23:160-175, 1971.
285. M. Pocchiola and G. Vegter. Minimal tangent visibility graphs. Computational Geometry: Theory and Applications, 6:303-314, 1996.
286. M. Pocchiola and G. Vegter. Topologically sweeping visibility complexes via pseudotriangulations. Discrete & Computational Geometry, 16:419-453, 1996.
287. M. Pocchiola and G. Vegter. The visibility complex. International Journal of Computational Geometry and Applications, 6:279-308, 1996.
288. R. Pollack, M. Sharir, and G. Vegter. Computing of the geodesic center of a simple polygon. Discrete & Computational Geometry, 4:611-626, 1989.
289. D. Prasad, S. P. Pal, and T. Dey. Visibility with multiple diffuse reflections. Computational Geometry: Theory and Applications, 10:187-196, 1998.
290. F. P. Preparata. A new approach to planar point location. SIAM Journal on Computing, 10:473-482, 1981.
291. F. P. Preparata and M. I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, New York, USA, 1990.
292. D. Rappaport. Computing simple circuits from a set of line segments is NP-complete. SIAM Journal on Computing, 18:1128-1139, 1989.
293. D. Rappaport, H. Imai, and G. T. Toussaint. Computing simple circuits from a set of line segments. Discrete & Computational Geometry, 5:289-304, 1990.
294. G. Rawlins. Explorations in Restricted-Orientation Geometry. Ph.D. Thesis, Universtiy of Waterloo, Waterloo, Ont., Canada, 1987.
295. G. Rawlins and D. Wood. Computational geometry with restricted orientations. In Proceedings of the 13th IFIP Conference on System Modelling and Optimization, Lecture Notes in Control and Information Science, volume 113, pages 375-384. Springer-Verlag, Berlin, Germany, 1988.
296. R. Reckhow and J. Culberson. Covering a simple orthogonal polygon with a minimum number of orthogonally convex polygons. In Proceedings of the 3rd Annua! ACM Symposium on Computational Geometry, pages 268-277. ACM Press, New York, USA, 1987.
297. J. H. Reif and J. A. Storer. Minimizing turns for discrete movement in the interior of a polygon. IEEE Journal on Robotics and Automation, RA-3:194-206, 1987.
298. H. Rohnert. Shortest paths in the plane with convex polygonal obstacles. Information Processing Letters, 23:71-76, 1986.
299. J.-R. Sack. An O(nlogn) algorithm for decomposing simple rectilinear polygons into quadrilaterals. In Proceedings of the 20th Allerton Conference, pages 64-75. Chicago, USA, 1982.
300. J.-R. Sack and S. Suri. An optimal algorithm for detecting weak visibility of a polygon. IEEE Transactions on Computers, 39:1213-1219, 1990.
301. J.-R. Sack and G. T. Toussaint. Guard placement in rectilinear polygons. In G. T. Toussaint, editor, Computational Morphology, pages 153-175. North-Holland, Amsterdam, The Netherlands, 1988.
302. N. Sarnak and R. E. Tarjan. Planar point location using persistent search trees. Communications of ACM, 29:669-679, 1986.
303. S. Schuierer. An optimal data structure for shortest rectilinear path queries in a simple rectilinear polygon. International Journal of Computational Geometry and Applications, 6:205-226, 1996.
304. S. Schuierer, G. Rawlins, and D. Wood. A generalization of staircase visibility. In Computational Geometry — Methods, Algorithms and Applications: Proc. Internat. Workshop Comput. Geom. CG’91, Lecture Notes in Computer Science, volume 553, pages 277-287. Springer-Verlag, Berlin, Germany, 1991.
305. S. Schuierer and D. Wood. Staircase visibility and computation of kernels. Algorithmica, 14:1-26, 1995.
306. L.G. Shapiro and R.M. Haralick. Decomposition of two-dimensional shape by graph- theoretic clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-1:10-19, 1979.
307. M. Sharir and A. Schorr. On shortest paths in polyhedral spaces. SIAM Journal on Computing, 15:193-215, 1986.
308. X. Shen and H. Edelsbrunner. A tight lower bound on the size of visibility graphs. Information Processing Letters, 26:61-64, 1987.
309. T. Shermer. Hiding people in polygons. Computing, 42:109-131, 1989.
310. T. Shermer. Recent results in art galleries. Proceedings of the IEEE, 80:1384-1399, 1992.
311. S. Y. Shin and T. C. Woo. An optimal algorithm for finding all visible edges in a simple polygon. IEEE Journal on Robotics and Automation, RA-5:202-207, 1989.
312. D. Sleator and R. E. Tarjan. Amortized efficiency of list update and paging rules. Communications of ACM, 28:202-208, 1985.
313. J. Spinrad, A. Brandstadt, and L. Stewart. Bipartite permutation graphs. Discrete Applied Mathematics, 18:279-292, 1987.
314. G. Srinivasaraghavan and A. Mukhopadhyay. A new necessary condition for the vertex visibility graphs of simple polygons. Discrete & Computational Geometry, 12:65-82, 1994.
315. G. Srinivasaraghavan and A. Mukhopadhyay. Orthogonal edge visibility graphs of polygons with holes. International Journal of Computational Geometry and Applications, 10:79-102, 2000.
316. I. Streinu. Non-stretchable pseudo-visibility graphs. In Proceedings of the 11th Canadian Conference on Computational Geometry, pages 22-25, 1999.
317. I. Streinu. Non-stretchable pseudo-visibility graphs. Computational Geometry: Theory and Applications, 31:195-206, 2005.
318. S. Suri. A linear time algorithm for minimum link paths inside a simple polygon. Computer Graphics, Vision, and Image Processing, 35:99-110, 1986.
319. S. Suri. Minimum link paths in polygons and related problems. Ph.D. Thesis, Department of Computer Science, Johns Hopkins University, Baltimore, MD, USA, 1987.
320. S. Suri. On some link distance problems in a simple polygon. IEEE Journal on Robotics and Automation, 6:108-113, 1990.
321. S. Suri and J. O’Rourke. Worst-case optimal algorithms for constructing visibility polygons with holes. In Proceedings of the 2nd Annual ACM Symposium on Computational Geometry, pages 14-23. ACM Press, New York, USA, 1986.
322. I. Suzuki, Y. Tazoe, M. Yamashita, and T. Kameda. Searching a polygonal region from the boundary. International Journal of Computational Geometry and Applications, 11:529-553, 2001.
323. I. Suzuki and M. Yamashita. Search for a mobile intruder in a polygonal region. SIAM Journal on Computing, 21:863-888, 1992.
324. I. Suzuki, M. Yamashita, H. Umemoto, and T. Kameda. Bushiness and a tight worst-case upper bound on the search number of a simple polygon. Information Processing Letters, 66:49-52, 1998.
325. R. Tamassia and I. Tollis. A unified approach to visibility representations of planar graphs. Discrete & Computational Geometry, 1:321-341, 1986.
326. R. E. Tarjan and C. J. Van Wyk. An O(n log log n)-time algorithm for triangulating a simple polygon. SIAM Journal on Computing, 17:143-178, 1988. Erratum in 17 (1988), 106.
327. H. Tietze. Uber konvexheit im kleinen und im grossen und uber gewisse den punkten einer menge zugeordnete dimensionszahlen. Math. Z., 28:679-707, 1929.
328. G. T. Tokarsky. Polygonal rooms not illuminable from every point. American Mathematical Monthly, 102:867-879, 1995.
329. G. T. Toussaint. An optimal algorithm for computing the minimum vertex distance between two crossing convex polygons. Computing, 32:357-364, 1984.
330. G. T. Toussaint. Shortest path solves edge-to-edge visibility in a polygon. Pattern Recognition Letters, 4:165-170, 1986.
331. G. T. Toussaint and D. Avis. On a convex hull algorithm for polygons and its application to triangulation problems. Pattern Recognition, 15:23-29, 1982.
332. L. H. Tseng, P. J. Heffernan, and D. T. Lee. Two-guard walkability of simple polygons. International Journal of Computational Geometry and Applications, 8:85-116, 1998.
333. J. Urrutia. Art gallery and illumination problems. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 973-1023. North-Holland, Amsterdam, The Netherlands, 2000.
334. F. A. Valentine. Convex Sets. McGraw-Hill, New York, USA, 1964.
335. G. Vegter. The visibility diagram: a data structure for visibility problems and motion planning. In Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, volume 447, pages 97-110. Springer-Verlag, Berlin, Germany, 1990.
336. C. A. Wang. Finding minimal nested polygons. BIT, 31:230-236, 1991.
337. C. A. Wang and E. P. F. Chan. Finding the minimum visible vertex distance between two nonintersecting simple polygons. In Proceedings of the 2nd Annua! ACM Symposium on Computational Geometry, pages 34-42. ACM Press, New York, USA, 1986.
338. R. Wein, P. den Berg, and D. Halperin. The visibility-Voronoi complex and its applications. In Proceedings of the 21th Annual ACM Symposium on Computational Geometry, pages 63-72. ACM Press, New York, USA, 2005.
339. 2) time. Information Processing Letters, 20:167-171, 1985.
340. S. K. Wismath. Characterizing bar line-of-sight graphs. In Proceedings of the 1st ACM Symposium on Computational Geometry, pages 147-152. ACM Press, New York, USA, 1985.
341. S. K. Wismath. Point and line segment reconstruction from visibility information. International Journal of Computational Geometry and Applications, 10:189-200, 2000.
342. T. C. Woo and S. Y. Shin. A linear time algorithm for triangulating a point-visible polygon. ACM Transactions of Graphics, 4:60-69, 1985.
343. D. Wood and P. Yamamoto. Dent and staircase visibility. In Proceedings of the 5th Canadian Conference on Computational Geometry, pages 297-302, 1993.
344. M. Yamashita, H. Umemoto, I. Suzuki, and T. Kameda. Searching for mobile intruders in a polygonal region by a group of mobile searchers. Algorithmica, 31:208-236, 2001.
345. C.-K. Yap. Parallel triangulation of a polygon in two calls to the trapezoidal map. Algorithmica, 3:279-288, 1988.
346. A. Zarei and M. Ghodsi. Efficient computation of query point visibility in polygons with holes. In Proceedings of the 21th Annual ACM Symposium on Computational Geometry, pages 314-320. ACM Press, New York, USA, 2005.
347. Z. Zhang. Applications of visibility space in polygon search problems. Ph.D. Thesis, School of Computing Science, Simon Fraser University, Burnaby, BC, Canada, 2005.