Abstract
We consider the fundamental problem of waking up n processors sharing a multiple access channel. We assume the weakest model of synchronization, the locally synchronous model, in which no global clock is available: processors have local clocks ticking at the same rate, but each clock starts counting the rounds in the round in which the correspondent processor wakes up. Moreover, the number n of processors is not known to the processors. We propose a new deterministic algorithm for this problem, which improves on the currently best upper bound.
Work supported in part by the European RTN Project under contract HPRN-CT-2002-00278,COMBSTRU.
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References
Bar-Yehuda, R., Goldreich, O., Itai, A.: On the Time-Complexity of Broadcast in Multi-hop Radio Networks: An Exponential Gap between Determinism and Randomization. Journal of Computer and System Sciences 45, 104–126 (1992)
Bertsekas, D., Gallager, R.: Data Networks. Prentice-Hall, Englewood Cliffs (1991)
Chrobak, M., Gasieniec, L., Kowalski, D.: The Wake-Up problem in multi-hop radio networks. In: Proceedings of 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), pp. 992–1000 (2004)
Chlebus, B., Gasieniec, L., Kowalski, D., Radzik, T.: On the Wake-up Problem in Radio Networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 347–359. Springer, Heidelberg (2005)
Chlebus, B., Kowalski, D.: A better wake-up in radio networks. In: Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing (PODC 2004), pp. 266–274 (2004)
De Bonis, A., Vaccaro, U.: Efficient Constructions of Generalized Superimposed Codes with Applications to Group Testing and Conflict Resolution in Multiple Access Channels. Theoretical Computer Science 306(1-3), 223–243 (2003)
De Marco, G., Pelc, A.: Faster broadcasting in unknown radio networks. Information Processing Letters 79, 53–56 (2001)
Du, D.Z., Hwang, F.K.: Combinatorial Group Testing and its Applications. World Scientific, Singapore (2000)
Erdös, P.: On the Integers Relatively Prime to n and on a Number-Theoretic Function Considered by Jacobsthal. Math. Scand. 11, 163–170 (1962)
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)
Gallager, R.: A Perspective on Multiaccess Channels. IEEE Trans. on Information Theory 31, 124–142 (1985)
Goodman, J., Greenberg, A.G., Madras, N., March, P.: On the stability of Ethernet. In: 17th ACM symposium on Theory of computing, STOC, pp. 379–387 (1985)
Ga̧sieniec, L., Pelc, A., Peleg, D.: The Wakeup Problem in Synchronous Broadcast Systems. SIAM J. Discrete Math. 14(2), 207–222 (2001)
Greenberg, A.G., Winograd, S.: A Lower Bound on the Time Needed in the Worst Case to Resolve Conflicts Deterministically in Multiple Access Channels. J. ACM 32, 596–598 (1985)
Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers, 4th edn. Clarendon Press, Oxford (1975)
Hastad, J., Leighton, T., Rogoff, B.: Analisys of Backoff Protocols for Multiple Access Channels. In: 19th ACM symposium on Theory of computing, STOC, pp. 241–253 (1987)
Indyk, P.: Deterministic Superimposed Coding with Application to Pattern Matching. In: 38th Symposium on Foundations of Computer Science, FOCS, pp. 127–136 (1997)
Iwaniec, H.: On the problem of Jacobstahl. Demonstratio Mathematica 11, 225–231 (1978)
Jurdziński, T., Stachowiak, G.: Probabilistic Algorithms for the Wakeup Problem in Single-Hop Radio Networks. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 535–549. Springer, Heidelberg (2002)
Komlós, J., Greenberg, A.G.: An Asymptotically Optimal Nonadaptive Algorithm for Conflict Resolution in Multiple-Access Channels. IEEE Trans. on Information Theory 31(2), 302–306 (1985)
Kautz, W.H., Singleton, R.C.: Nonrandom binary superimposed codes. IEEE Trans. Inform. Theory 10, 363–377 (1964)
Tannenbaum, A.: Computer Networks. Prentice-Hall, Englewood Cliffs (1981)
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De Marco, G., Pellegrini, M., Sburlati, G. (2005). Faster Deterministic Wakeup in Multiple Access Channels. In: Coppo, M., Lodi, E., Pinna, G.M. (eds) Theoretical Computer Science. ICTCS 2005. Lecture Notes in Computer Science, vol 3701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11560586_16
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DOI: https://doi.org/10.1007/11560586_16
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