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Emergent Computation pp 71–99Cite as

On the Microscopic View of Time and Messages

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Part of the book series: Emergence, Complexity and Computation ((ECC,volume 24))

Abstract

In distributed message-passing systems, synchronous computations rely on and exploit for their correctness and/or efficiency the existence of some reliable mechanism, which provides all system entities with a globally consistent view of time, e.g., a common global clock. Many of these computations, however, exploit time at a macroscopic level: they assume that transmission of an unbounded amount of information can be done in constant time. We are instead interested in the microscopic level of synchronous computations; that is, the study of computability and complexity when, in a constant amount of time, only a constant number of bits can be transmitted. Our general interest includes the extreme case, when a message contains only a single bit. We discuss the basics of computing at the microscopic level, describing simple but powerful computational tools, and analyzing their use.

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Notes

  1. 1.

    These intervals are usually assumed to have all the same length, but such a condition is not necessary.

References

  1. Alimonti, P., Flocchini, P., Santoro, N.: Finding the extrema of a distributed multiset of values. J. Parallel Distrib. Comput. 37, 123–133 (1996)

    Article  MATH  Google Scholar 

  2. Alon, N., Babai, L., Itai, A.: A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algorithms 7(4), 567–583 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  3. Angluin, D.: Local and global properties in networks of processes. In: Proceedings of the 12th ACM Symposium on Theory of Computing (STOC), pp. 82–93 (1980)

    Google Scholar 

  4. Arora, A., Dolev, S., Gouda, M.: Maintaining digital clocks in step. Parallel Process. Lett. 1(1), 11–18 (1991)

    Article  Google Scholar 

  5. Attiya, H., Snir, M., Warmuth, M.K.: Computing on an anonymous ring. J. ACM 35(4), 845–875 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bar-Noy, A., Naor, J., Naor, M.: One bit algorithms. Distrib. Comput. 4(1), 3–8 (1990)

    Article  MathSciNet  Google Scholar 

  7. Bar-Noy, A., Dolev, D.: Consensus algorithms with one-bit messages. Distrib. Comput. 4(3), 105–110 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bodlaender, H.L., Tel, G.: Bit-optimal election in synchronous rings. Inf. Process. Lett. 36(1):53–64 (1990)

    Google Scholar 

  9. Elkin, M.: A faster distributed protocol for constructing a minimum spanning tree. J. Comput. Syst. Sci. 72(8), 1282–1308 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Even, S., Rajsbaum, S.: Unison, canon and sluggish clocks in networks controlled by a synchronizer. Math. Syst. Theor. 28, 421–435 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  11. Frederickson, G.N., Santoro, N.: Breaking symmetry in synchronous networks. In: Proceedings of 2nd International Workshop on Parallel Computing and VLSI (now SPAA), pp. 26–33 (1986)

    Google Scholar 

  12. Frederickson, G.N., Lynch, N.A.: Electing a leader in a synchronous ring. J. ACM 34, 95–115 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gafni, E.: Improvements in the time complexity of two message-optimal election algorithms. In: Proceedings of the 4th Conference on Principles of Distributed Computing (PODC), pp. 175–185 (1985)

    Google Scholar 

  14. Garay, J., Kutten, S., Peleg, D.: A sub-linear time distributed algorithm for minimum-weight spanning trees. SIAM J. Comput. 27, 302–316 (1998)

    Article  MATH  Google Scholar 

  15. Goldberg, A.V., Plotkin, S.A., Shannon, G.E.: Parallel symmetry-breaking in sparse graphs. SIAM J. Discr. Math. 1(4), 434–446 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gouda, M., Herman, T.: Stabilizing unison. Inf. Process. Lett. 35(4), 171–175 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  17. Halldórsson, M.M., Konrad, C.: Distributed large independent sets in one round on bounded-independence graphs. In: Proceedings of the 29th International Symposium on Distributed Computing (DISC), pp. 559–572 (2015)

    Google Scholar 

  18. Israeli, A., Kranakis, E., Krizanc, D., Santoro, N.: Time-messages tradeoffs for the weak unison problem. Nordic J. Comput. 4, 317–329 (1997)

    MathSciNet  MATH  Google Scholar 

  19. Israeli, A., Itai, A.: A fast and simple randomized parallel algorithm for maximal matching. Inf. Process. Lett. 22, 77–80 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  20. Itai, A., Rodeh, M.: Symmetry breaking in distributed networks. Inf. Comput. 88(1), 60871 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  21. Jia, L., Rajaraman, R., Suel, T.: An efficient distributed algorithm for constructing small dominating sets. Distrib. Comput. 15(4), 193–205 (2002)

    Article  Google Scholar 

  22. Kothapalli, K., Onus, M., Scheideler, C., Schindelhauer, C.: Distributed coloring in \(O(\sqrt{\log n})\) bit rounds. In: Proceedings of the 20th International Parallel and Distributed Processing Symposium (IPDPS) (2006)

    Google Scholar 

  23. Kutten, S., Peleg, D.: Fast distributed construction of k-dominating sets and applications. J. Algorithms 28, 40–66 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  24. Lotker, Z., Patt-Shamir, B., Pavlov, E., Peleg, D.: Minimum-weight spanning tree construction in \(O(\log \log n)\) communication rounds. SIAM J. Comput. 35(1), 120–131 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. Marchetti-Spaccamela, A.: New protocols for the election of a leader in a ring. Theor. Comput. Sci. 54(1), 53–64 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  26. Mayer, A., Ofek, Y., Ostrovsky, R., Yung, M.: Self-stabilizing symmetry breaking in constant-space. In: Proceedings of the 24th ACM Symposium on Theory of Computing (STOC), pp. 667–678 (1992)

    Google Scholar 

  27. Métivier, Y., Robson, J.M., Saheb-Djahromi, N., Zemmari, A.: An optimal bit complexity randomized distributed MIS algorithm. Distrib. Comput. 23(5–6), 331–340 (2011)

    Article  MATH  Google Scholar 

  28. Métivier, Y., Robson, J.M., Zemmari, A.: A distributed enumeration algorithm and applications to all pairs shortest paths, diameter. Inf. Comput. 247, 141–151 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  29. Nishitani, Y., Honda, N.: The firing squad synchronization problem for graphs. Theor. Comput. Sci. 14, 39–61 (198I)

    Google Scholar 

  30. O’Reilly, U.-M., Santoro, N.: Asynchronous to synchronous transformations. In: Proceedings of the 4th International Conference on Principles of Distributed Systems (OPODIS), pp. 265–282 (2000)

    Google Scholar 

  31. O’Reilly, U.-M., Santoro, N.: Tight bound for synchronous communication of information using bits and silence. Discret. Appl. Math. 129, 195–209 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  32. Ostrovsky, R., Wilkersan, D.S.: Faster computation on directed networks of automata. In: Proceedings of the 14th ACM Symposium on Principles of Distributed Computing (PODC), pp. 38–46 (1995)

    Google Scholar 

  33. Overmars, M., Santoro, N.: Improved bounds for electing a leader in a synchronous ring. Algorithmica 18, 246–262 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  34. Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM (2000)

    Google Scholar 

  35. Santoro, N., Rotem, D.: On the complexity of distributed elections in synchronous graphs. In: Proceedings of the 11th International Workshop on Graphtheoretic Concepts in Computer Science (WG), pp. 337–346 (1985)

    Google Scholar 

  36. Santoro, N.: Computing with time: temporal dimensions in distributed computing. In: Proceedings of the 28th Allerton Conference on Communication, Control and Computing, pp. 558–567 (1990)

    Google Scholar 

  37. Santoro, N.: Design and Analysis of Distributed Algorithms. Wiley (2007)

    Google Scholar 

  38. Schmeltz, B.: Optimal tradeoffs between time and bit complexity in synchronous rings. In: Proceedings of the 7th Symposium on Theoretical Aspects of Computer Science (STACS), pp. 275–284 (1990)

    Google Scholar 

  39. Schneider, J., Wattenhofer, R.: Trading bit, message, and time complexity of distributed algorithms. In: Proceedings of the 25th International Symposium on Distributed Computing (DISC), pp. 51–65 (2011)

    Google Scholar 

  40. Spirakis, P., Tampakas, B.: Efficient distributed algorithms by using the Archimedean time assumption. Informatique Théorique et Applications 23(1), 113–128 (1989)

    MathSciNet  MATH  Google Scholar 

  41. van Leeuwen, J., Santoro, N., Urrutia, J., Zaks, S.: Guessing games and distributed computations in anonymous networks. In: Proceedings of the 14th International Colloquium on Automata, Languages and Programming (ICALP), pp. 347–356 (1987)

    Google Scholar 

  42. Wattenhofer, M., Wattenhofer, R.: Distributed weighted matching. In: Proceedings of the 18th International Symposium on Distributed Computing (DISC), pp. 335–348 (2004)

    Google Scholar 

  43. Xu, L., Jeavons, P.: Simple algorithms for distributed leader election in anonymous synchronous rings and complete networks inspired by neural development fruit flies. Int. J. Neural Syst. 25(7) (2015)

    Google Scholar 

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Acknowledgments

This work has been supported in part by the Natural Sciences and Engineering Research Council (Canada) under the Discovery Grant program.

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  1. School of Computer Science, Carleton University, Ottawa, Canada

    Nicola Santoro

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  1. Nicola Santoro
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Correspondence to Nicola Santoro .

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  1. Unconventional Computing Centre, University of the West of England Unconventional Computing Centre, Bristol, United Kingdom

    Andrew Adamatzky

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Santoro, N. (2017). On the Microscopic View of Time and Messages. In: Adamatzky, A. (eds) Emergent Computation . Emergence, Complexity and Computation, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-46376-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-46376-6_5

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