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2015 | OriginalPaper | Buchkapitel

On the Relations Between SINR Diagrams and Voronoi Diagrams

verfasst von : Merav Parter, David Peleg

Erschienen in: Ad-hoc, Mobile, and Wireless Networks

Verlag: Springer International Publishing

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Abstract

In this review, we illustrate the relations between wireless communication and computational geometry. As a concrete example, we consider a fundamental geometric object from each field: SINR diagrams and Voronoi diagrams. We discuss the relations between these representations, which appear in several distinct settings of wireless communication, as well as some algorithmic applications.

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Literatur
1.
Zurück zum Zitat Andrews, J.G.: Interference cancellation for cellular systems: a contemporary overview. IEEE Wirel. Commun. 12(2), 19–29 (2005)CrossRef Andrews, J.G.: Interference cancellation for cellular systems: a contemporary overview. IEEE Wirel. Commun. 12(2), 19–29 (2005)CrossRef
2.
Zurück zum Zitat Andrews, M., Dinitz, M.: Maximizing capacity in arbitrary wireless networks in the SINR model: complexity and game theory. In: Proceedings of the INFOCOM (2009) Andrews, M., Dinitz, M.: Maximizing capacity in arbitrary wireless networks in the SINR model: complexity and game theory. In: Proceedings of the INFOCOM (2009)
3.
Zurück zum Zitat Aronov, B., Katz, M.J.: Batched point location in SINR diagrams via algebraic tools. CoRR, abs/1412.0962 (2014) Aronov, B., Katz, M.J.: Batched point location in SINR diagrams via algebraic tools. CoRR, abs/1412.0962 (2014)
4.
Zurück zum Zitat Aurenhammer, F., Edelsbrunner, H.: An optimal algorithm for constructing the weighted voronoi diagram in the plane. Pattern Recogn. 17, 251–257 (1984)MATHMathSciNetCrossRef Aurenhammer, F., Edelsbrunner, H.: An optimal algorithm for constructing the weighted voronoi diagram in the plane. Pattern Recogn. 17, 251–257 (1984)MATHMathSciNetCrossRef
5.
Zurück zum Zitat Avin, C., Cohen, A., Haddad, Y., Kantor, E., Lotker, Z., Parter, M., Peleg, D.: SINR diagram with interference cancellation. In: Proceedings of the SODA, pp. 502–515 (2012) Avin, C., Cohen, A., Haddad, Y., Kantor, E., Lotker, Z., Parter, M., Peleg, D.: SINR diagram with interference cancellation. In: Proceedings of the SODA, pp. 502–515 (2012)
6.
Zurück zum Zitat Avin, C., Emek, Y., Kantor, E., Lotker, Z., Peleg, D., Roditty, L.: SINR diagrams: convexity and its applications in wireless networks. J. ACM 59(4), 18:1–18:34 (2012)MathSciNetCrossRef Avin, C., Emek, Y., Kantor, E., Lotker, Z., Peleg, D., Roditty, L.: SINR diagrams: convexity and its applications in wireless networks. J. ACM 59(4), 18:1–18:34 (2012)MathSciNetCrossRef
7.
Zurück zum Zitat Avin, C., Lotker, Z., Pignolet, Y.-A.: On the power of uniform power: capacity of wireless networks with bounded resources. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 373–384. Springer, Heidelberg (2009) CrossRef Avin, C., Lotker, Z., Pignolet, Y.-A.: On the power of uniform power: capacity of wireless networks with bounded resources. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 373–384. Springer, Heidelberg (2009) CrossRef
8.
Zurück zum Zitat Baccelli, F., Blaszczyszyn, B.: Stochastic geometry and wireless networks volume 1: theory. Found. Trends Network. 3, 249–449 (2009)MATHCrossRef Baccelli, F., Blaszczyszyn, B.: Stochastic geometry and wireless networks volume 1: theory. Found. Trends Network. 3, 249–449 (2009)MATHCrossRef
9.
Zurück zum Zitat Costa, M., El-Gamal, A.: The capacity region of the discrete memoryless interference channel with strong interference. IEEE Trans. Inf. Th. 33, 710–711 (1987)MATHMathSciNetCrossRef Costa, M., El-Gamal, A.: The capacity region of the discrete memoryless interference channel with strong interference. IEEE Trans. Inf. Th. 33, 710–711 (1987)MATHMathSciNetCrossRef
10.
11.
Zurück zum Zitat Edelsbrunner, H., Kirkpatrick, D., Seidel, R.: On the shape of a set of points in the plane. IEEE Trans. Inf. Th. 29(4), 551–559 (1983)MATHMathSciNetCrossRef Edelsbrunner, H., Kirkpatrick, D., Seidel, R.: On the shape of a set of points in the plane. IEEE Trans. Inf. Th. 29(4), 551–559 (1983)MATHMathSciNetCrossRef
12.
Zurück zum Zitat Etkin, R.H., Tse, D.N.C., Wang, H.: Gaussian interference channel capacity to within one bit. IEEE Trans. Inf. Th. 54(12), 5534–5562 (2008)MATHMathSciNetCrossRef Etkin, R.H., Tse, D.N.C., Wang, H.: Gaussian interference channel capacity to within one bit. IEEE Trans. Inf. Th. 54(12), 5534–5562 (2008)MATHMathSciNetCrossRef
13.
Zurück zum Zitat Goldsmith, A.: Wireless Communications. Cambridge University Press, Cambridge (2005)CrossRef Goldsmith, A.: Wireless Communications. Cambridge University Press, Cambridge (2005)CrossRef
14.
Zurück zum Zitat Goussevskaia, O., Wattenhofer, R., Halldórsson, M.M., Welzl, E.: Capacity of arbitrary wireless networks. In: Proceedings of the INFOCOM, pp. 1872–1880 (2009) Goussevskaia, O., Wattenhofer, R., Halldórsson, M.M., Welzl, E.: Capacity of arbitrary wireless networks. In: Proceedings of the INFOCOM, pp. 1872–1880 (2009)
16.
Zurück zum Zitat Halldórsson, M.M., Wattenhofer, R.: Wireless communication is in APX. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 525–536. Springer, Heidelberg (2009) CrossRef Halldórsson, M.M., Wattenhofer, R.: Wireless communication is in APX. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 525–536. Springer, Heidelberg (2009) CrossRef
17.
Zurück zum Zitat Kantor, E., Lotker, Z., Parter, M., Peleg, D.: The topology of wireless communication. In: Proceedings of the STOC (2011) Kantor, E., Lotker, Z., Parter, M., Peleg, D.: The topology of wireless communication. In: Proceedings of the STOC (2011)
18.
Zurück zum Zitat Moscibroda, T.: The worst-case capacity of wireless sensor networks. In: Proceedings of the IPSN, pp. 1–10 (2007) Moscibroda, T.: The worst-case capacity of wireless sensor networks. In: Proceedings of the IPSN, pp. 1–10 (2007)
19.
Zurück zum Zitat Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tesselations. Princeton University Press, Princeton (1992) Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tesselations. Princeton University Press, Princeton (1992)
20.
Zurück zum Zitat Ozgur, A., Leveque, O., Tse, D.: Hierarchical cooperation achieves optimal capacity scaling in ad hoc networks. IEEE Trans. Inf. Th. 53, 3549–3572 (2007)MathSciNetCrossRef Ozgur, A., Leveque, O., Tse, D.: Hierarchical cooperation achieves optimal capacity scaling in ad hoc networks. IEEE Trans. Inf. Th. 53, 3549–3572 (2007)MathSciNetCrossRef
21.
Zurück zum Zitat Sato, H.: The capacity of the gaussian interference channel under strong interference. IEEE Trans. Inf. Th. 27(6), 786–788 (1981)MATHCrossRef Sato, H.: The capacity of the gaussian interference channel under strong interference. IEEE Trans. Inf. Th. 27(6), 786–788 (1981)MATHCrossRef
22.
Zurück zum Zitat Tse, D., Viswanath, P.: Fundamentals of Wireless Communication. Cambridge University Press, Cambridge (2005)MATHCrossRef Tse, D., Viswanath, P.: Fundamentals of Wireless Communication. Cambridge University Press, Cambridge (2005)MATHCrossRef
23.
Zurück zum Zitat Viterbi, A.J.: Very low rate convolution codes for maximum theoretical performance of spread-spectrum multiple-access channels. IEEE J. Sel. Areas Commun. 8(4), 641–649 (1990)CrossRef Viterbi, A.J.: Very low rate convolution codes for maximum theoretical performance of spread-spectrum multiple-access channels. IEEE J. Sel. Areas Commun. 8(4), 641–649 (1990)CrossRef
Metadaten
Titel
On the Relations Between SINR Diagrams and Voronoi Diagrams
verfasst von
Merav Parter
David Peleg
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-19662-6_16