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Interference in Cellular Networks: The Minimum Membership Set Cover Problem

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Computing and Combinatorics (COCOON 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3595))

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Abstract

The infrastructure for mobile distributed tasks is often formed by cellular networks. One of the major issues in such networks is interference. In this paper we tackle interference reduction by suitable assignment of transmission power levels to base stations. This task is formalized introducing the Minimum Membership Set Cover combinatorial optimization problem. On the one hand we prove that in polynomial time the optimal solution of the problem cannot be approximated more closely than with a factor ln n. On the other hand we present an algorithm exploiting linear programming relaxation techniques which asymptotically matches this lower bound.

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References

  1. Chvátal, V.: A Greedy Heuristic for the Set-Covering Problem. Mathematics of Operations Research 4(3), 233–235 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  2. Even, G., Lotker, Z., Ron, D., Smorodinsky, S.: Conflict-Free Colorings of Simple Geometric Regions with Applications to Frequency Assignment in Cellular Networks. In: 43rd Annual IEEE Symposium on Foundations of Computer Science, FOCS (2002)

    Google Scholar 

  3. Feige, U.: A Threshold of ln n for Approximating Set Cover. Journal of the ACM (JACM) 45(4), 634–652 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fortuin, C., Kasteleyn, P., Ginibre, J.: Correlations Inequalities on Some Partially Ordered Sets. Comm. Math. Phys. 22, 89–103 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  5. Harris, T.E.: A Lower Bound for the Critical Probability in a Certain Percolation Process. Proc. Cambridge Philos. Soc. 60, 13–20 (1960)

    Article  Google Scholar 

  6. Janssen, J.: Channel Assignment and Graph Labeling. In: Stojmenovic, I. (ed.) Handbook of Wireless Networks and Mobile Computing, ch. 5, pp. 95–117. John Wiley & Sons, Inc., Chichester (2002)

    Chapter  Google Scholar 

  7. Johnson, D.: Approximation algorithms for combinatorial problems. Journal of Computer and System Sciences 9, 256–278 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kleitman, D.: Families of Non-Disjoint Subsets. Journal of Combinatorial Theory 1, 153–155 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lu, C.-J.: A Deterministic Approximation Algorithm for a Minimax Integer Programming Problem. In: Proc. of the 10th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 663–668 (1999)

    Google Scholar 

  10. Lund, C., Yannakakis, M.: On the Hardness of Approximating Minimization Problems. Journal of the ACM 41(5), 960–981 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  11. Narayanan, L.: Channel Assignment and Graph Multicoloring. In: Stojmenovic, I. (ed.) Handbook of Wireless Networks and Mobile Computing, ch. 4, pp. 71–94. John Wiley & Sons, Inc., Chichester (2002)

    Chapter  Google Scholar 

  12. Raghavan, P., Thompson, C.: Randomized Rounding: A Technique for Provably Good Algorithms and Algorithmic Proofs. Combinatorica 7(4), 365–374 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  13. Srinivasan, A.: Improved Approximations of Packing and Covering Problems. In: Proc. of the 27th ACM Symposium on Theory of Computing, pp. 268–276 (1995)

    Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Kuhn, F., von Rickenbach, P., Wattenhofer, R., Welzl, E., Zollinger, A. (2005). Interference in Cellular Networks: The Minimum Membership Set Cover Problem. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_21

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  • DOI: https://doi.org/10.1007/11533719_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28061-3

  • Online ISBN: 978-3-540-31806-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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