Abstract
We obtain a polynomial time approximation scheme for the terrain guarding problem improving upon several recent constant factor approximations. Our algorithm is a local search algorithm inspired by the recent results of Chan and Har-Peled [2] and Mustafa and Ray [15]. Our key contribution is to show the existence of a planar graph that appropriately relates the local and global optimum.
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Ben-Moshe, B., Katz, M.J., Mitchell, J.S.B.: A constant-factor approximation algorithm for optimal terrain guarding. In: SODA, pp. 515–524 (2005)
Chan, T., Har-Peled, S.: Approximation algorithms for maximum independent set of pseudo-disks. In: Symposium on Computational Geometry (to appear, 2009)
Chen, D.Z., Estivill-Castro, V., Urrutia, J.: Optimal guarding of polygons and monotone chains (extended abstract) (1996)
Clarkson, K.L., Varadarajan, K.: Improved approximation algorithms for geometric set cover. In: SCG 2005: Proceedings of the twenty-first annual symposium on Computational geometry, pp. 135–141. ACM Press, New York (2005)
Deshpande, A., Kim, T., Demaine, E.D., Sarma, S.E.: A pseudopolynomial time o(log2 n)-approximation algorithm for art gallery problems. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 163–174. Springer, Heidelberg (2007)
Efrat, A., Har-Peled, S.: Guarding galleries and terrains. Information Processing Letters 100(6), 238–245 (2006)
Eidenbenz, S.: Inapproximability results for guarding polygons without holes. LNCS, pp. 427–436. Springer, Heidelberg (1998)
Elbassioni, K., Krohn, E., Matijevic, D., Mestre, J., Severdija, D.: Improved approximations for guarding 1.5-dimensional terrains. In: Albers, S., Marion, J.-Y. (eds.) 26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009), Dagstuhl, Germany, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany (2009)
Erlebach, T., Jansen, K., Seidel, E.: Polynomial-time approximation schemes for geometric intersection graphs. SIAM Journal on Computing 34(6), 1302–1323 (2005)
Frederickson, G.N.: Fast algorithms for shortest paths in planar graphs, with applications. SIAM J. Comput. 16(6), 1004–1022 (1987)
Ghosh, S.: Approximation algorithms for art gallery problems. In: Proc. Canadian Information Processing Society Congress (1987)
King, J.: A 4-approximation algorithm for guarding 1.5-dimensional terrains. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 629–640. Springer, Heidelberg (2006)
Krohn, E., King, J.: The complexity of guarding terrains (manuscript, 2009)
Lee, D., Lin, A.: Computational complexity of art gallery problems. IEEE Transactions on Information Theory 32(2), 276–282 (1986)
Mustafa, N.H., Ray, S.: Ptas for geometric hitting set problems via local search. In: Symposium on Computational Geometry (to Appear, 2009)
Nilsson, B.J.: Approximate guarding of monotone and rectilinear polygons. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1362–1373. Springer, Heidelberg (2005)
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Gibson, M., Kanade, G., Krohn, E., Varadarajan, K. (2009). An Approximation Scheme for Terrain Guarding. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_11
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DOI: https://doi.org/10.1007/978-3-642-03685-9_11
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