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Stable Leader Election in Population Protocols Requires Linear Time

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Distributed Computing (DISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9363))

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Abstract

A population protocol stably elects a leader if, for all n, starting from an initial configuration with n agents each in an identical state, with probability 1 it reaches a configuration y that is correct (exactly one agent is in a special leader state \(\ell \)) and stable (every configuration reachable from y also has a single agent in state \(\ell \)). We show that any population protocol that stably elects a leader requires \(\Omega (n)\) expected “parallel time” — \(\Omega (n^2)\) expected total pairwise interactions — to reach such a stable configuration. Our result also informs the understanding of the time complexity of chemical self-organization by showing an essential difficulty in generating exact quantities of molecular species quickly.

D. Doty—Author was supported by NSF grants CCF-1219274 and CCF-1442454 and the Molecular Programming Project under NSF grant 1317694.

D. Soloveichik—Author was supported by an NIGMS Systems Biology Center grant P50 GM081879 and NSF grant CCF-1442454.

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References

  1. Alistarh, D., Gelashvili, R.: Polylogarithmic-time leader election in population protocols. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 479–491. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  2. Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distributed Computing 18, 235–253 (2006). http://dx.doi.org/10.1007/s00446-005-0138-3, preliminary version appeared in PODC 2004

    Article  MATH  Google Scholar 

  3. Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Urn automata. Tech. Rep. YALEU/DCS/TR-1280, Yale University, November 2003

    Google Scholar 

  4. Angluin, D., Aspnes, J., Eisenstat, D.: Fast computation by population protocols with a leader. Distributed Computing 21(3), 183–199 (2008). preliminary version appeared in DISC 2006

    Article  MATH  Google Scholar 

  5. Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: The computational power of population protocols. Distributed Computing 20(4), 279–304 (2007)

    Article  MATH  Google Scholar 

  6. Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. In: Anderson, J.H., Prencipe, G., Wattenhofer, R. (eds.) OPODIS 2005. LNCS, vol. 3974, pp. 103–117. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Bower, J.M., Bolouri, H.: Computational modeling of genetic and biochemical networks. MIT press (2004)

    Google Scholar 

  8. Chen, H.-L., Cummings, R., Doty, D., Soloveichik, D.: Speed faults in computation by chemical reaction networks. In: Kuhn, F. (ed.) DISC 2014. LNCS, vol. 8784, pp. 16–30. Springer, Heidelberg (2014). http://dx.doi.org/10.1007/978-3-662-45174-8_2

    Google Scholar 

  9. Chen, H.L., Doty, D., Soloveichik, D.: Deterministic function computation with chemical reaction networks. Natural Computing 13(4), 517–534 (2014). preliminary version appeared in DISC 2012

    Article  MathSciNet  Google Scholar 

  10. Chen, Y.J., Dalchau, N., Srinivas, N., Phillips, A., Cardelli, L., Soloveichik, D., Seelig, G.: Programmable chemical controllers made from DNA. Nature Nanotechnology 8(10), 755–762 (2013)

    Article  Google Scholar 

  11. Cunha-Ferreira, I., Bento, I., Bettencourt-Dias, M.: From zero to many: control of centriole number in development and disease. Traffic 10(5), 482–498 (2009)

    Article  Google Scholar 

  12. Dickson, L.E.: Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. American Journal of Mathematics 35(4), 413–422 (1913)

    Article  MATH  MathSciNet  Google Scholar 

  13. Doty, D.: Timing in chemical reaction networks. In: SODA 2014: Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 772–784, January 2014

    Google Scholar 

  14. Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81(25), 2340–2361 (1977)

    Article  Google Scholar 

  15. Karp, R.M., Miller, R.E.: Parallel program schemata. Journal of Computer and System Sciences 3(2), 147–195 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  16. Petri, C.A.: Communication with automata. Tech. rep, DTIC Document (1966)

    Google Scholar 

  17. Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. Proceedings of the National Academy of Sciences 107(12), 5393 (2010). preliminary version appeared in DISC 2008

    Article  Google Scholar 

  18. Volterra, V.: Variazioni e fluttuazioni del numero dindividui in specie animali conviventi. Mem. Acad. Lincei Roma 2, 31–113 (1926)

    Google Scholar 

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Author information

Authors and Affiliations

  1. University of California, Davis, Davis, CA, USA

    David Doty

  2. University of Texas at Austin, Austin, TX, USA

    David Soloveichik

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  1. David Doty
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  2. David Soloveichik
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Correspondence to David Soloveichik .

Editor information

Editors and Affiliations

  1. Technion, Haifa, Israel

    Yoram Moses

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Doty, D., Soloveichik, D. (2015). Stable Leader Election in Population Protocols Requires Linear Time. In: Moses, Y. (eds) Distributed Computing. DISC 2015. Lecture Notes in Computer Science(), vol 9363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48653-5_40

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  • DOI: https://doi.org/10.1007/978-3-662-48653-5_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48652-8

  • Online ISBN: 978-3-662-48653-5

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