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Art gallery theorems and algorithms
Art gallery theorems and algorithms
The Art Gallery theorem for polygons with holes
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The art gallery theorem: its variations, applications and algorithmic aspects
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On guarding the vertices of rectilinear domains
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Fast vertex guarding for polygons with and without holes
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Guarding thin orthogonal polygons is hard
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Unsolved problems in visibility graphs of points, segments, and polygons
ACM Computing Surveys (CSUR)
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In this paper, we present approximation algorithms for minimum vertex and edge guard problems for polygons with or without holes with a total of n vertices. For simple polygons, approximation algorithms for both problems run in O(n^4) time and yield solutions that can be at most O(logn) times the optimal solution. For polygons with holes, approximation algorithms for both problems give the same approximation ratio of O(logn), but the running time of the algorithms increases by a factor of n to O(n^5).