Skip to main content
SpringerLink
Log in

Network Design under General Wireless Interference

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

We introduce the problem of finding a spanning tree along with a partition of the tree edges into the fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we seek to model the irregularities seen in actual wireless environments. Not all node pairs may be able to communicate, even if geographically close—thus, the available pairs are specified with a link graph \({{\mathcal {G}}}=(V,E)\). Also, signal attenuation need not follow a nice geometric formula—hence, interference is modeled by a conflict (hyper)graph \({{\mathcal {C}}}=(E,F)\) on the links. The objective is to maximize the efficiency of the communication, or equivalently, to minimize the length of a schedule of the tree edges in the form of a coloring. We find that in spite of all this generality, the problem can be approximated linearly in terms of a versatile parameter, the inductive independence of the conflict graph. Specifically, we give a simple algorithm that attains a \(O(\rho \log n)\)-approximation, where n is the number of nodes and \(\rho\) is the inductive independence. For an extension to Steiner trees, modeling multicasting, we obtain a \(O(\rho \log ^2 n)\)-approximation. We also consider a natural geometric setting when only links longer than a threshold can be unavailable, and analyze the performance of a geometric minimum spanning tree.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  1. Akcoglu, K., Aspnes, J., DasGupta, B., Kao, M.Y.: Opportunity cost algorithms for combinatorial auctions. In: Computational Methods in Decision-Making, Economics and Finance, pp. 455–479. Springer (2002)

  2. Baccour, N., Koubaa, A., Mottola, L., Zuniga, M.A., Youssef, H., Boano, C.A., Alves, M.: Radio link quality estimation in wireless sensor networks: a survey. ACM Trans. Sens. Netw. 8(4), 34 (2012)

    Article  Google Scholar 

  3. Bilò V, Caragiannis, I., Fanelli, A., Flammini, M., Monaco, G.: Simple greedy algorithms for fundamental multidimensional graph problems. In: ICALP, pp 125:1–125:13 (2017)

  4. Bodlaender, M.H.L., Halldórsson, M.M.: Beyond geometry: towards fully realistic wireless models. In: PODC, pp 347–356 (2014)

  5. Dams, J., Hoefer, M., Kesselheim, T.: Scheduling in wireless networks with Rayleigh-fading interference. IEEE Trans. Mob. Comput. 14(7), 1503–1514 (2015)

    Article  Google Scholar 

  6. Fanghänel, A., Kesselheim, T., Räcke, H., Vöcking, B.: Oblivious interference scheduling. In: PODC, pp 220–229 (2009)

  7. Feige, U., Kilian, J.: Zero knowledge and the chromatic number. J. Comput. Syst. Sci. 57, 187–199 (1998)

    Article  MathSciNet  Google Scholar 

  8. Fürer, M., Raghavachari, B.: Approximating the minimum-degree Steiner tree to within one of optimal. J. Algorithms 17(3), 409–423 (1994)

    Article  MathSciNet  Google Scholar 

  9. Gandhi, R., Halldórsson, M.M., Konrad, C., Kortsarz, G., Oh, H.: Radio aggregation scheduling. In: ALGOSENSORS, pp 169–182 (2015)

  10. Ganesan, D., Krishnamachari, B., Woo, A., Culler, D., Estrin, D., Wicker, S.: Complex behavior at scale: an experimental study of low-power wireless sensor networks, p. 02. Tech. rep, UCLA/CSD-TR (2002)

  11. Göbel, O., Hoefer, M., Kesselheim, T., Schleiden, T., Vöcking, B.: In: Online independent set beyond the worst-case: secretaries, prophets, and periods. In: ICALP, pp. 508–519 (2014)

  12. Goldsmith, A.: Wireless Communications. Cambridge University Press (2005)

  13. Goussevskaia, O., Halldórsson, M.M., Wattenhofer, R.: Algorithms for wireless capacity. IEEE/ACM Trans. Netw. 22(3), 745–755 (2014)

    Article  Google Scholar 

  14. Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Trans. Inf. Theory 46(2), 388–404 (2000)

    Article  MathSciNet  Google Scholar 

  15. Halldórsson, M.M.: Wireless scheduling with power control. ACM Trans. Algorithms 9(1), 7 (2012)

    Article  MathSciNet  Google Scholar 

  16. Halldórsson, M.M., Mitra, P.: Wireless capacity with oblivious power in general metrics. In: SODA, pp. 1538–1548 (2011)

  17. Halldórsson, M.M., Mitra, P.: Wireless connectivity and capacity. In: SODA, pp. 516–526 (2012)

  18. Halldórsson, M.M., Mitra, P.: Nearly optimal bounds for distributed wireless scheduling in the SINR model. Distrib. Comput. 29(2), 77–88 (2016)

    Article  MathSciNet  Google Scholar 

  19. Halldórsson, M.M., Tonoyan, T.: How well can graphs represent wireless interference? In: STOC, pp. 635–644 (2015)

  20. Halldórsson, M.M, Tonoyan, T.: The price of local power control in wireless scheduling. In: FSTTCS, pp. 529–542 (2015)

  21. Halldórsson, M.M., Tonoyan, T.: Wireless link capacity under shadowing and fading. In: MobiHoc, pp. 27:1–27:10 (2017)

  22. Halldórsson, M.M., Tonoyan, T.: Wireless aggregation at nearly constant rate. In: ICDCS, pp. 753–763 (2018)

  23. Halldórsson, M.M., Holzer, S., Mitra, P., Wattenhofer, R.: The power of oblivious wireless power. SIAM J. Comput. 46(3), 1062–1086 (2017)

    Article  MathSciNet  Google Scholar 

  24. Halldórsson, M.M., Tonoyan, T.: Computing inductive vertex orderings. Inf. Process. Lett. 172, 106159 (2021). https://doi.org/10.1016/j.ipl.2021.106159

    Article  MathSciNet  MATH  Google Scholar 

  25. Hoefer, M., Kesselheim, T.: Secondary spectrum auctions for symmetric and submodular bidders. ACM Trans. Econ. Comput. 3(2), 9 (2015)

    Article  MathSciNet  Google Scholar 

  26. Hoefer, M., Kesselheim, T., Vöcking, B.: Approximation algorithms for secondary spectrum auctions. ACM Trans. Internet Technol. 14(2–3), 16 (2014)

    Google Scholar 

  27. Incel, Ö.D., Ghosh, A.A., Krishnamachari, B.: Scheduling algorithms for tree-based data collection in wireless sensor networks. In: Nikoletseas, S.E., Rolim, J.D.P. (eds.) Theoretical Aspects of Distributed Computing in Sensor Networks, Monographs in Theoretical Computer Science, An EATCS Series, pp. 407–445. Springer (2011)

  28. Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9, 256–278 (1974)

    Article  MathSciNet  Google Scholar 

  29. Kesselheim, T.: A constant-factor approximation for wireless capacity maximization with power control in the SINR model. In: SODA, pp. 1549–1559 (2011)

  30. Kesselheim, T.: Approximation algorithms for wireless link scheduling with flexible data rates. In: ESA, pp. 659–670 (2012)

  31. Kesselheim, T.: Dynamic packet scheduling in wireless networks. In: PODC, pp. 281–290 (2012)

  32. Kesselheim, T., Vöcking, B.: Distributed contention resolution in wireless networks. In: DISC, pp. 163–178 (2010)

  33. Kotz, D., Newport, C., Gray, R.S., Liu, J., Yuan, Y., Elliott, C.: Experimental evaluation of wireless simulation assumptions. In: MSWiM, pp. 78–82 (2004)

  34. Kruskal, J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Am. Math. Soc. 7(1), 48–50 (1956)

    Article  MathSciNet  Google Scholar 

  35. Kuhn, F., Lynch, N., Newport, C., Oshman, R., Richa, A.: Broadcasting in unreliable radio networks. In: PODC, pp. 336–345 (2010)

  36. Moscibroda, T.: The worst-case capacity of wireless sensor networks. In: IPSN, pp. 1–10 (2007)

  37. Moscibroda, T., Wattenhofer, R.: The complexity of connectivity in wireless networks. In: INFOCOM (2006)

  38. Moscibroda, T., Wattenhofer, R., Zollinger, A.: Topology control meets SINR: the scheduling complexity of arbitrary topologies. In: MOBIHOC, pp. 310–321 (2006)

  39. Son, D., Krishnamachari, B., Heidemann, J.: Experimental study of concurrent transmission in wireless sensor networks. In: SenSys, ACM, pp. 237–250 (2006)

  40. Ye, Y., Borodin, A.: Elimination graphs. ACM Trans. Algorithms 8(2), 14:1–14:23 (2012)

  41. Zamalloa, M.Z., Krishnamachari, B.: An analysis of unreliability and asymmetry in low-power wireless links. ACM Trans. Sens. Netw. 3(2), 7 (2007)

    Article  Google Scholar 

Download references

Funding

Funding was provided by Icelandic Centre for Research (Grant No. 174484-051).

Author information

Authors and Affiliations

  1. ICE-TCS, Department of Computer Science, Reykjavik University, Reykjavík, Iceland

    Magnús M. Halldórsson

  2. Department of Computer Science, Rutgers University, Camden, NJ, USA

    Guy Kortsarz

  3. Google Research, New York, NY, USA

    Pradipta Mitra

  4. Department of Computer Science, Technion Israel Institute of Technology, Haifa, Israel

    Tigran Tonoyan

Authors
  1. Magnús M. Halldórsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guy Kortsarz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pradipta Mitra
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tigran Tonoyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tigran Tonoyan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Halldórsson, M.M., Kortsarz, G., Mitra, P. et al. Network Design under General Wireless Interference. Algorithmica 83, 3469–3490 (2021). https://doi.org/10.1007/s00453-021-00866-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-021-00866-z

Keywords

Search

Navigation