Abstract
Consider a scenario where base stations need to send data to users with wireless devices. Time is discrete and slotted into synchronous rounds. Transmitting a data item from a base station to a user takes one round. A user can receive the data item from any of the base stations. The positions of the base stations and users are modeled as points in Euclidean space. If base station b transmits to user u in a certain round, no other user within distance at most ||b − u||2 from b can receive data in the same round due to interference phenomena. The goal is to minimize, given the positions of the base stations and users, the number of rounds until all users have their data.
We call this problem the Joint Base Station Scheduling Problem (JBS) and consider it on the line (1D-JBS) and in the plane (2D-JBS). For 1D-JBS, we give a 2-approximation algorithm and polynomial optimal algorithms for special cases. We model transmissions from base stations to users as arrows (intervals with a distinguished endpoint) and show that their conflict graphs, which we call arrow graphs, are a subclass of the class of perfect graphs. For 2D-JBS, we prove NP-hardness and discuss an approximation algorithm.
Research partially supported by TH-Project TH-46/02-1 (Mobile phone antenna optimization: theory, algorithms, engineering, and experiments).
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References
Brandstädt, A., Le, V.B., Spinrad, J.P.: Graph classes: A survey. In: SIAM Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics, Philadelphia, PA (1999)
Chuzhoy, J., Naor, S.: New hardness results for congestion minimization and machine scheduling. In: Proceedings of the 36th Annual ACM Symposium on the Theory of Computing (STOC 2004), pp. 28–34 (2004)
Cielibak, M., Erlebach, T., Hennecke, F., Weber, B., Widmayer, P.: Scheduling jobs on a minimum number of machines. In: Proceedings of the 3rd IFIP International Conference on Theoretical Computer Science, pp. 217–230. Kluwer, Dordrecht (2004)
Das, S., Viswanathan, H., Rittenhouse, G.: Dynamic load balancing through coordinated scheduling in packet data systems. In: Proceedings of Infocom 2003 (2003)
Erlebach, T., Jacob, R., Mihaľák, M., Nunkesser, M., Szabó, G., Widmayer, P.: Joint base station scheduling. Technical Report 461, ETH Zürich, Institute of Theoretical Computer Science (2004)
Erlebach, T., Spieksma, F.C.R.: Interval selection: Applications, algorithms, and lower bounds. Algorithmica 46, 27–53 (2001)
Felsner, S., Müller, R., Wernisch, L.: Trapezoid graphs and generalizations, geometry and algorithms. Discrete Applied Mathematics 74, 13–32 (1997)
Garey, M.R., Johnson, D.S.: Computers and Intractability, Freeman (1979)
Gräf, A., Stumpf, M., Weißenfels, G.: On coloring unit disk graphs. Algorithmica 20(3), 277–293 (1998)
Grötschel, M., Lovász, L., Schrijver, A.: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1, 169–197 (1981)
Khachiyan, L.: A polynomial algorithm in linear programming. Doklady Akademii Nauk SSSR 244, 1093–1096 (1979)
Spieksma, F.C.R.: On the approximability of an interval scheduling problem. Journal of Scheduling 2, 215–227 (1999)
Spinrad, J.P.: Efficient Graph Representations. Field Institute Monographs. AMS 19 (2003)
West, D.: Introduction to Graph Theory, 2nd edn. Prentice Hall, Englewood Cliffs (2001)
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Erlebach, T., Jacob, R., Mihaľák, M., Nunkesser, M., Szabó, G., Widmayer, P. (2005). Joint Base Station Scheduling. In: Persiano, G., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2004. Lecture Notes in Computer Science, vol 3351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31833-0_19
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DOI: https://doi.org/10.1007/978-3-540-31833-0_19
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