Abstract
Given a set of wireless links, a fundamental problem is to find the largest subset that can transmit simultaneously, within the SINR model of interference. Significant progress on this problem has been made in recent years. In this note, we study the problem in the setting where we are given a fixed set of arbitrary powers each sender must use, and an arbitrary gain matrix defining how signals fade. This variation of the problem appears immune to most algorithmic approaches studied in the literature. Indeed it is very hard to approximate since it generalizes the max independent set problem. Here, we propose a simple semi-definite programming approach to the problem that yields constant factor approximation, if the optimal solution is strictly larger than half of the input size.
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References
Chafekar, D., Kumar, V., Marathe, M., Parthasarathy, S., Srinivasan, A.: Cross-layer Latency Minimization for Wireless Networks using SINR Constraints. In: Mobihoc (2007)
Chlamtac, E.: Approximation algorithms using hierarchies of semidefinite programming relaxations. In: FOCS, pp. 691–701. IEEE Computer Society (2007)
Chlamtac, E., Singh, G.: Improved Approximation Guarantees through Higher Levels of SDP Hierarchies. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 49–62. Springer, Heidelberg (2008)
Dams, J., Hoefer, M., Kesselheim, T.: Convergence Time of Power-Control Dynamics. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 637–649. Springer, Heidelberg (2011)
Fanghänel, A., Kesselheim, T., Räcke, H., Vöcking, B.: Oblivious interference scheduling. In: PODC, pp. 220–229 (August 2009)
Fanghänel, A., Keßelheim, T., Vöcking, B.: Improved Algorithms for Latency Minimization in Wireless Networks. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 447–458. Springer, Heidelberg (2009)
Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42, 1115–1145 (1995)
Goussevskaia, O., Halldórsson, M.M., Wattenhofer, R., Welzl, E.: Capacity of Arbitrary Wireless Networks. In: INFOCOM, pp. 1872–1880 (April 2009)
Grant, M., Boyd, S.: CVX: Matlab software for disciplined convex programming, version 1.21. (April 2011), http://cvxr.com/cvx
Grönkvist, J., Hansson, A.: Comparison between graph-based and interference-based STDMA scheduling. In: Mobihoc, pp. 255–258 (2001)
Halldórsson, M.M., Mitra, P.: Nearly Optimal Bounds for Distributed Wireless Scheduling in the SINR Model. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 625–636. Springer, Heidelberg (2011)
Halldórsson, M.M., Mitra, P.: Wireless Capacity with Oblivious Power in General Metrics. In: SODA (2011)
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. LNCS, vol. 5555, pp. 525–536. Springer, Heidelberg (2009)
Halperin, E.: Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs. In: SODA, pp. 329–337 (2000)
Halperin, E., Nathaniel, R., Zwick, U.: Coloring k-colorable graphs using relatively small palettes. J. Algorithms 45, 72–90 (2002)
Kantor, E., Lotker, Z., Parter, M., Peleg, D.: The Topology of Wireless Communication. In: STOC (2011)
Karakostas, G.: A better approximation ratio for the vertex cover problem. ACM Trans. Algorithms 5, 41:1–41:8 (2009)
Karger, D., Motwani, R., Sudan, M.: Approximate graph coloring by semidefinite programming. J. ACM 45, 246–265 (1998)
Kesselheim, T.: A Constant-Factor Approximation for Wireless Capacity Maximization with Power Control in the SINR Model. In: SODA (2011)
Kesselheim, T., Vöcking, B.: Distributed Contention Resolution in Wireless Networks. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 163–178. Springer, Heidelberg (2010)
Krivelevich, M., Nathaniel, R., Sudakov, B.: Approximating coloring and maximum independent sets in 3-uniform hypergraphs. In: SODA, pp. 327–328 (2001)
Maheshwari, R., Jain, S., Das, S.R.: A measurement study of interference modeling and scheduling in low-power wireless networks. In: SenSys, pp. 141–154 (2008)
Hoefer, M., Thomas Kesselheim, B.V.: Approximation Algorithms for Secondary Spectrum Auctions. In: SPAA (2011)
Moscibroda, T., Wattenhofer, R.: The Complexity of Connectivity in Wireless Networks. In: INFOCOM (2006)
Moscibroda, T., Oswald, Y.A., Wattenhofer, R.: How optimal are wireless scheduling protocols? In: INFOCOM, pp. 1433–1441 (2007)
Moscibroda, T., Wattenhofer, R., Weber, Y.: Protocol Design Beyond Graph-Based Models. In: Hotnets (November 2006)
Moscibroda, T., Wattenhofer, R., Zollinger, A.: Topology Control meets SINR: The Scheduling Complexity of Arbitrary Topologies. In: MOBIHOC, pp. 310–321 (2006)
Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Review 38, 49–95 (1994)
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Halldórsson, M.M., Mitra, P. (2012). Wireless Capacity with Arbitrary Gain Matrix. In: Erlebach, T., Nikoletseas, S., Orponen, P. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2011. Lecture Notes in Computer Science, vol 7111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28209-6_17
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DOI: https://doi.org/10.1007/978-3-642-28209-6_17
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