Feedback from nature: An optimal distributed algorithm for maximal independent set selection

Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

Volumn , Issue , 2013, Pages 147-156

  Scott, Alex ^a   Jeavons, Peter ^a   Xu, Lei ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Beeping model; Expected complexity; Feedback; Intercellular signalling; Message complexity; MIS; Randomised algorithms

Indexed keywords

EXPECTED COMPLEXITY; INTERCELLULAR SIGNALLING; MAXIMAL INDEPENDENT SET; MESSAGE COMPLEXITY; NEIGHBOURING NODES; OPTIMAL EFFICIENCY; PROBABILISTIC ALGORITHM; RANDOMISED ALGORITHMS;

COMPLEX NETWORKS; FEEDBACK; MANAGEMENT INFORMATION SYSTEMS; OPTIMIZATION;

ALGORITHMS;

EID: 84883535817     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2484239.2484247     Document Type: Conference Paper

References (21)

1. Y. Afek, N. Alon, Z. Bar-Joseph, A. Cornejo, B. Haeupler, and F. Kuhn. Beeping a maximal independent set. In Proceedings of the 25th international conference on Distributed Computing, DISC'11, pages 32-50, Berlin, Heidelberg, 2011. Springer-Verlag.
2. Y. Afek, N. Alon, O. Barad, E. Hornstein, N. Barkai, and Z. Bar-Joseph. A biological solution to a fundamental distributed computing problem. Science, 331(6014): 183-185, 2011.
3. N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7: 577-583, December 1986.
4. O. Barad, E. Hornstein, and N. Barkai. Robust selection of sensory organ precursors by the Notch-Delta pathway. Current Opinion in Cell Biology, 23(6): 663-667, 2011.
5. O. Barad, D. Rosin, E. Hornstein, and N. Barkai. error minimization in lateral inhibition circuits. Science Signaling, 3(129): ra51, 2010.
6. S. J. Bray. Notch signalling: a simple pathway becomes complex. Nature reviews. Molecular cell biology, 7(9): 678-689, Sept. 2006.
7. J. R. Collier, N. A. M. Monk, P. K. Maini, and J. H. Lewis. Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling. Journal of Theoretical Biology, 183(4): 429-446, 1996.
8. R. Ghosh and C. J. Tomlin. Lateral inhibition through Delta-Notch signaling: a piecewise affine hybrid model. In Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control, HSCC '01, pages 232-246, London, UK, 2001. Springer-Verlag.
9. K. G. Guruharsha, M. W. Kankel, and S. Artavanis-Tsakonas. The Notch signalling system: recent insights into the complexity of a conserved pathway. Nature Reviews. Genetics, 13(9): 654-666, Sept. 2012.
10. 1-e. Acta Mathematica, 8: 105-142, 1999.
11. T. L. Jacobsen, K. Brennan, A. M. Arias, and M. A. T. Muskavitch. Cis-interactions between Delta and Notch modulate neurogenic signalling in Drosophila. Development, 125(22): 4531-40, 1998.
12. R. M. Karp. Reducibility among combinatorial problems. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, The IBM Research Symposia Series, pages 85-103. Plenum Press, New York, 1972.
13. F. Kuhn, T. Moscibroda, T. Nieberg, and R. Wattenhofer. Fast deterministic distributed maximal independent set computation on growth-bounded graphs. In P. Fraigniaud, editor, Distributed Computing: 19th International Conference, DISC 2005, Volume 3724 of Lecture Notes in Computer Science, pages 273-283, Berlin, November 2005. Springer-Verlag.
14. F. Kuhn, T. Moscibroda, and R. Wattenhofer. The price of being near-sighted. In Proceedings of the 17th annual ACM-SIAM Symposium on Discrete Algorithms, SODA '06, pages 980-989, New York, NY, USA, 2006.
15. N. Linial. Locality in distributed graph algorithms. SIAM Journal on Computing, 21(1): 193-201, Feb. 1992.
16. M. Luby. A simple parallel algorithm for the maximal independent set problem. In Proceedings of the seventeenth annual ACM Symposium on Theory of Computing, STOC '85, pages 1-10, New York, NY, USA, 1985.
17. M. Matsuda and A. B. Chitnis. Interaction with Notch determines endocytosis of specific Delta ligands in zebrafish neural tissue. Development, 136(2): 197-206, 2009.
18. Y. Métivier, J. M. Robson, N. Saheb-Djahromi, and A. Zemmari. An optimal bit complexity randomized distributed MIS algorithm. Distributed Computing, 3: 331-340, 2011.
19. T. Moscibroda and R. Wattenhofer. Maximal independent sets in radio networks. In Proceedings of the 24th annual ACM Symposium on Principles of Distributed Computing, PODC '05, pages 148-157, New York, NY, USA, 2005.
20. S. Navlakha and Z. Bar-Joseph. Algorithms in nature: the convergence of systems biology and computational thinking. Molecular Systems Biology, 7(1), Nov. 2011.
21. D. Sprinzak, A. Lakhanpal, L. LeBon, L. A. Santat, M. E. Fontes, G. A. Anderson, J. Garcia-Ojalvo, and M. B. Elowitz. Cis-interactions between Notch and Delta generate mutually exclusive signalling states. Nature, 465(7294): 86-90, Apr. 2010.