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Wireless Coverage via Dynamic Programming

  • Conference paper
Wireless Algorithms, Systems, and Applications (WASA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6843))

Abstract

Coverage has been one of the most fundamental yet challenging issues in wireless networks and found many applications, such as routing and broadcasting. Given a set of weighted unit disks (coverage areas) and a set of nodes to be covered, we study the minimum weight coverage problem under two specific topologies. The first one assumes that the centers of the disks lie inside a strip while the nodes lie outside of this strip. The second topology assumes that the centers of the disks lie within a unit circle while the nodes lie outside of this circle. For each topology, we present a polynomial-time algorithm to find a disk subset of minimum total weight to cover all nodes. Both of our algorithms relies on dynamic programming.

This work was supported in part by NSF of USA under grant CNS-0831831.

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References

  1. Abrams, Z., Goel, A., Plotkin, S.: Set k-cover algorithms for energy efficient monitoring in wireless sensor networks. In: Proceedings of the 3rd International Symposium on Information Processing in Sensor Networks, pp. 424–432. ACM, New York (2004)

    Google Scholar 

  2. Ambühl, C., Erlebach, T., Mihalák, M., Nunkesser, M.: Constant-Factor Approximation for Minimum-Weight (Connected) Dominating Sets in Unit Disk Graphs. In: Díaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds.) APPROX 2006 and RANDOM 2006. LNCS, vol. 4110, pp. 3–14. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Baysan, M., Sarac, K., Chandrasekaran, R., Bereg, S.: A Polynomial Time Solution to Minimum Forwarding Set Problem in Wireless Networks under Unit Disk Coverage Model. IEEE Transactions on Parallel and Distributed Systems, 913–924 (2008)

    Google Scholar 

  4. Br”onnimann, H., Goodrich, M.: Almost optimal set covers in finite VC-dimension. Discrete and Computational Geometry 14(1), 463–479 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  5. Călinescu, G., Mandoiu, I., Wan, P., Zelikovsky, A.: Selecting forwarding neighbors in wireless ad hoc networks. Mobile Networks and Applications 9(2), 101–111 (2004)

    Article  Google Scholar 

  6. Carmi, P., Katz, M., Lev-Tov, N.: Covering points by unit disks of fixed location. Algorithms and Computation, 644–655 (2007)

    Google Scholar 

  7. Dai, D., Yu, C.: A 5 + ε-approximation algorithm for minimum weighted dominating set in unit disk graph. Theoretical Computer Science 410(8-10), 756–765 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Erlebach, T., Mihalák, M.: A (4+ ε)-Approximation for the Minimum-Weight Dominating Set Problem in Unit Disk Graphs. Approximation and Online Algorithms, 135–146 (2010)

    Google Scholar 

  9. Gonzalez, T.: Covering a set of points in multidimensional space* 1. Information Processing Letters 40(4), 181–188 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hochbaum, D., Maass, W.: Approximation schemes for covering and packing problems in image processing and VLSI. Journal of the ACM (JACM) 32(1), 130–136 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hou, J., Yau, D., Ma, C., Yang, Y., Zhang, H., Hou, I., Rao, N., Shankar, M.: Coverage in wireless sensor networks. Guide to Wireless Sensor Networks, 47–79 (2009)

    Google Scholar 

  12. Huang, Y., et al.: A better constant-factor approximation for weighted dominating set in unit disk graph. J. Comb. Optim. 1382, 6905 (2008)

    Google Scholar 

  13. Johnson, D.: The NP-completeness column: an ongoing guide. Journal of Algorithms 13(3), 502–524 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  14. Narayanappa, S., Vojtechovskỳ, P.: An improved approximation factor for the unit disk covering problem. In: Proc. Can. Conf. on Comp. Geom., Citeseer (2006)

    Google Scholar 

  15. Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pp. 475–484. ACM, New York (1997)

    Google Scholar 

  16. Wan, P., Xu, X., Wang, Z.: Wireless Coverage with Disparate Ranges. In: ACM MobiHoc (2011)

    Google Scholar 

  17. Wan, P., Yi, C.: Coverage by randomly deployed wireless sensor networks. IEEE Transactions on Information Theory 52, 2658–2669 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang, J., Zhong, N.: Efficient point coverage in wireless sensor networks. Journal of Combinatorial Optimization 11(3), 291–304 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wu, J., Lou, W.: Forward-node-set-based broadcast in clustered mobile ad hoc networks. Wireless Communications and Mobile Computing 3(2), 155–173 (2003)

    Article  Google Scholar 

  20. Yun, Z., Bai, X., Xuan, D., Lai, T., Jia, W.: Optimal Deployment Patterns for Full Coverage and k-Connectivity (k ≤ 6) Wireless Sensor Networks. IEEE/ACM Transactions on Networking 18(3) (2010)

    Google Scholar 

  21. Zou, F., Wang, Y., Xu, X., Li, X., Du, H., Wan, P., Wu, W.: New approximations for minimum-weighted dominating sets and minimum-weighted connected dominating sets on unit disk graphs. Theoretical Computer Science (2011)

    Google Scholar 

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Xu, X., Wang, Z. (2011). Wireless Coverage via Dynamic Programming. In: Cheng, Y., Eun, D.Y., Qin, Z., Song, M., Xing, K. (eds) Wireless Algorithms, Systems, and Applications. WASA 2011. Lecture Notes in Computer Science, vol 6843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23490-3_10

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  • DOI: https://doi.org/10.1007/978-3-642-23490-3_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23489-7

  • Online ISBN: 978-3-642-23490-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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