Approximate Guarding of Monotone and Rectilinear Polygons

被引：15
|
作者：
Krohn, Erik A. [1 ]
Nilsson, Bengt J. [2 ]
机构：
[1] Univ Wisconsin, Dept Comp Sci, Oshkosh, WI 54901 USA
[2] Malmo Univ, Dept Comp Sci, S-20506 Malmo, Sweden
来源：
ALGORITHMICA | 2013年 / 66卷 / 03期
关键词：
Computational geometry; Art gallery problems; Monotone polygons; Rectilinear polygons; Approximation algorithms; ART GALLERY PROBLEMS; VISIBILITY POLYGON; ALGORITHM;
D O I：
10.1007/s00453-012-9653-3
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We show that vertex guarding a monotone polygon is NP-hard and construct a constant factor approximation algorithm for interior guarding monotone polygons. Using this algorithm we obtain an approximation algorithm for interior guarding rectilinear polygons that has an approximation factor independent of the number of vertices of the polygon. If the size of the smallest interior guard cover is OPT for a rectilinear polygon, our algorithm produces a guard set of size O(OPT (2)).
引用
收藏
页码：564 / 594
页数：31
相关论文
共 50 条
  • [1] Approximate Guarding of Monotone and Rectilinear Polygons
    Erik A. Krohn
    Bengt J. Nilsson
    [J]. Algorithmica, 2013, 66 : 564 - 594
  • [2] Approximate guarding of monotone and rectilinear polygons
    Nilsson, BJ
    [J]. AUTOMATA, LANGUAGES AND PROGRAMMING, PROCEEDINGS, 2005, 3580 : 1362 - 1373
  • [3] Generalized guarding and partitioning for rectilinear polygons
    Gyori, E
    Hoffmann, F
    Kriegel, K
    Shermer, T
    [J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 1996, 6 (01): : 21 - 44
  • [4] Altitude terrain guarding and guarding uni-monotone polygons
    Daescu, Ovidiu
    Friedrichs, Stephan
    Malik, Hemant
    Polishchuk, Valentin
    Schmidt, Christiane
    [J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2019, 84 : 22 - 35
  • [5] Rectilinear Duals Using Monotone Staircase Polygons
    Chang, Yi-Jun
    Yen, Hsu-Chun
    [J]. COMBINATORIAL OPTIMIZATION AND APPLICATIONS (COCOA 2014), 2014, 8881 : 86 - 100
  • [6] On guarding rectilinear domains
    Katz, Matthew J.
    Roisman, Gabriel S.
    [J]. ALGORITHM THEORY - SWAT 2006, PROCEEDINGS, 2006, 4059 : 220 - 231
  • [7] Evacuation of Rectilinear Polygons
    Fekete, Sandor
    Gray, Chris
    Kroeller, Alexander
    [J]. COMBINATORIAL OPTIMIZATION AND APPLICATIONS, PT 1, 2010, 6508 : 21 - 30
  • [8] On guarding the vertices of rectilinear domains
    Katz, Matthew J.
    Roisman, Gabriel S.
    [J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2008, 39 (03): : 219 - 228
  • [9] Triangulating and guarding realistic polygons
    Aloupis, Greg
    Bose, Prosenjit
    Dujmovic, Vida
    Gray, Chris
    Langerman, Stefan
    Speckmann, Bettina
    [J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2014, 47 (02): : 296 - 306
  • [10] Edge guards in rectilinear polygons
    Bjorling-Sachs, I
    [J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 1998, 11 (02): : 111 - 123
12345