Skip to main content

A New Kind of Selectors and Their Applications to Conflict Resolution in Wireless Multichannels Networks

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 10050))

Abstract

We investigate the benefits of using multiple channels of communications in wireless networks, under the full-duplex multi-packet reception model of communication. The main question we address is the following: Is a speedup linear in the number of channels achievable, for some interesting communication primitive? We provide a positive answer to this interrogative for the Information Exchange Problem, in which k arbitrary nodes have information they intend to share with the entire network. To achieve this goal, we devise and exploit a combinatorial structure that generalizes well known combinatorial tools widely used in the area of data-exchange in multiple access channels (i.e., strongly selective families, selectors, and related mathematical objects). For our new combinatorial structures we provide both existential results, based on the Lovász Local Lemma, and efficient constructions, leveraging on properties of error correcting codes. We also prove non existential results, showing that our constructions are not too far from being optimal.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. I.802.11 Wireless LAN MAC and Physical Layer Specification. http://www.ieee802.org/

  2. Alon, N., Spencer, J.H.: The probabilistic method. In: Wiley-Interscience Series in Discrete Mathematics and Optimization, 3rd edn. Wiley, Hoboken (2008)

    Google Scholar 

  3. Alon, N., Asodi, V.: Learning a hidden subgraph. SIAM J. Discrete Math. 18, 697–712 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Avgouleas, I., Angelakis, V., Pappas, N.: Utilizing multiple full-duplex relays in wireless systems with multiple packet reception. In: 19th IEEE International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD), pp. 193–197 (2014)

    Google Scholar 

  5. Boneh, D., Shaw, J.: Collusion-free fingerprinting for digital data. IEEE Trans. Inf. Theory 44, 1897–1905 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bluetooth Consortium: Bluetooth Specification. https://www.bluetooth.com/

  7. Clementi, A.E.F., Monti, A., Silvestri, R.: Distributed broadcast in radio networks of unknown topology. Theor. Comput. Sci. 302(1–3), 337–364 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chlamtac, I., Faragó, A.: An optimal channel access protocol with multiple reception capacity. IEEE Trans. Comput. 43, 480–484 (1994)

    Article  Google Scholar 

  9. Chlebus, B.S.: Randomized communication in radio networks. In: Pardalos, P.M., Rajasekaran, S., Reif, J.H., Roli, J.D.P. (eds.) Handbook on Randomized Computing, vol. 1, pp. 401–456. Kluwer Academic Publishers (2001)

    Google Scholar 

  10. Chrobak, M., Ga̧sieniec, L., Rytter, W.: Fast broadcasting and fast broadcasting and gossiping in radio networks. J. Algorithms 43(2), 177–189 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Cohen, G.D.: Applications of coding theory to communication combinatorial problems. Discrete Math. 83(2–3), 237–248 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  12. Csűrös, M., Ruszinkó, M.: Single-user tracing and disjointly superimposed codes. IEEE Trans. Inf. Theory 51(4), 1606–1611 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Daum, S., Kuhn, F., Newport, C.: Efficient symmetry breaking in multi-channel radio networks. DISC 2012, 238–252 (2012)

    MathSciNet  MATH  Google Scholar 

  14. De Bonis, A., Ga̧sieniec, L., Vaccaro, U.: Optimal two-stage algorithms for group testing problems. SIAM J. Comput. 34(5), 1253–1270 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Dolev, S., Gilbert, S., Khabbazian, M., Newport, C.: Leveraging channel diversity to gain efficiency and robustness for wireless broadcast. In: Peleg, D. (ed.) DISC 2011. LNCS, vol. 6950, pp. 252–267. Springer, Berlin (2011). doi:10.1007/978-3-642-24100-0_25

    Chapter  Google Scholar 

  16. Du, D.Z., Hwang, F.K.: Combinatorial Group Testing and Its Applications. World Scientific, River Edge (2000)

    MATH  Google Scholar 

  17. D’yachkov, A.G., Rykov, V.V.: Bounds on the length of disjunct codes. Problemy Peredachi Informatsii 18(3), 7–13 (1982)

    MathSciNet  MATH  Google Scholar 

  18. D’yachkov, A.G., Vorobév, I.V., Polyansky, N.A., Yu, V.: Shchukin: bounds on the rate of disjunctive codes. Probl. Inf. Transm. 50(1), 27–56 (2014)

    Article  MathSciNet  Google Scholar 

  19. D’yachkov, A.G., Vorobév, I.V., Polyansky, N.A., Yu, V.: Shchukin: erratum to: bounds on the rate of disjunctive codes. Probl. Inf. Transm. 50, 27 (2014). Problems of Information Transmission, 52(2), 200 (2016)

    Article  MathSciNet  Google Scholar 

  20. Erdös, P., Frankl, P., Füredi, Z.: Families of finite sets in which no set is covered by the union of \(r\) others. Israel J. Math. 51, 75–89 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  21. Füredi, Z.: On \(r\)-cover-free families. J. Comb. Theory Ser. A 73, 172–173 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  22. Gyory, S.: Coding for a multiple access OR channel: a survey. Discrete Appl. Math. 156, 1407–1430 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Halldórsson, M., Wang, Y., Yu, D.: Leveraging multiple channels in ad hoc networks. In: PODC 2015, pp. 431–440 (2015)

    Google Scholar 

  24. Holzer, S., Pignolet, Y., Smula, J., Wattenhofer, R.: Time-optimal information exchange on multiple channels. In: FOMC 2011, pp. 69–76 (2011)

    Google Scholar 

  25. Kautz, W.H., Singleton, R.C.: Nonrandom binary superimposed codes. IEEE Trans Inf. Theory 10, 363–377 (1964)

    Article  MATH  Google Scholar 

  26. Khasin, L.S.: Conflict resolution in a multiple access channel. Probl. Peredachi Inf. 25(4), 63–68 (1989)

    MathSciNet  MATH  Google Scholar 

  27. Komlós, J., Greenberg, A.G.: An asymptotically fast non-adaptive algorithm for conflict resolution in multiple-access channels. IEEE Trans. Inf. Theory 31(2), 302–306 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  28. Kowalski, D.R.: On selection problem in radio networks. In: PODC 2005, pp. 158–166. ACM Press (2005)

    Google Scholar 

  29. Krishnaswamy, H., Zussman, G.: 1 chip, 2\(\times \) the bandwidth. IEEE Spectr. 53(7), 38–54 (2016)

    Article  Google Scholar 

  30. Massey, J.L., Mathys, P.: The collision channel without feedback. IEEE Trans. Inf. Theory 31, 192–204 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  31. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North Holland Publishing Co., Amsterdam (1977)

    MATH  Google Scholar 

  32. Moser, R.A., Tardos, G.: A constructive proof of the general Lovász local lemma. J. ACM 57, 11–15 (2010)

    Article  MATH  Google Scholar 

  33. Pappas, N., Kountouris, M., Ephremides, A., Traganitis, A.: Relay-assisted multiple access with full-duplex multi-packet reception. IEEE Trans. Wirel. Commun. 14, 3544–3558 (2015)

    Article  Google Scholar 

  34. Ruszinkó, M.: On the upper bound of the size of the \(r\)-cover-free families. J. Comb. Theory Ser. A 66, 302–310 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  35. Staddon, J.N., Stinson, D.R., Wei, R.: Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inf. Theory 47, 1042–1049 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  36. Stinson, D.R., Wei, R., Chen, K.: On generalized separating hash families. J. Comb. Theory Ser. A 115, 105–120 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  37. Stinson, D.R., Zaverucha, G.M.: Some improved bounds for secure frameproof codes and related separating hash families. IEEE Trans. Inf. Theory 54, 2508–2514 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  38. Stinson, D.R., Wei, R., Zhu, L.: New constructions for perfect hash families and related structures using combinatorial designs and codes. J. Comb. Des. 8, 189–200 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  39. Yan, Y., Yu, D., Wang, Y., Yu, J., Lau, F.C.: Bounded information dissemination in multi-channel wireless networks. J. Comb. Optim. 31, 996–1012 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  40. Yu, D., Wang, Y., Yan, Y., Yu, J., Lau, F.C.: Speedup of information exchange using multiple channels in wireless ad hoc networks. In: 2015 IEEE Conference on Computer Communication (INFOCOM), pp. 2029–20137 (2015)

    Google Scholar 

  41. Wang, Y., Wang, Y., Yu, D., Yu, J., Lau, F.C.: Information exchange with collision detection on multiple channels. J. Comb. Optim. 31, 118–135 (2016)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Annalisa De Bonis .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

De Bonis, A., Vaccaro, U. (2017). A New Kind of Selectors and Their Applications to Conflict Resolution in Wireless Multichannels Networks. In: Chrobak, M., Fernández Anta, A., Gąsieniec, L., Klasing, R. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2016. Lecture Notes in Computer Science(), vol 10050. Springer, Cham. https://doi.org/10.1007/978-3-319-53058-1_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-53058-1_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53057-4

  • Online ISBN: 978-3-319-53058-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics