Joint Base Station Scheduling
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.
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- 1.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)Google Scholar
- 2.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)Google Scholar
- 3.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)Google Scholar
- 4.Das, S., Viswanathan, H., Rittenhouse, G.: Dynamic load balancing through coordinated scheduling in packet data systems. In: Proceedings of Infocom 2003 (2003)Google Scholar
- 5.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)Google Scholar
- 8.Garey, M.R., Johnson, D.S.: Computers and Intractability, Freeman (1979)Google Scholar
- 13.Spinrad, J.P.: Efficient Graph Representations. Field Institute Monographs. AMS 19 (2003)Google Scholar
- 14.West, D.: Introduction to Graph Theory, 2nd edn. Prentice Hall, Englewood Cliffs (2001)Google Scholar