Stably Computable Properties of Network Graphs

  • Dana Angluin
  • James Aspnes
  • Melody Chan
  • Michael J. Fischer
  • Hong Jiang
  • René Peralta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3560)


We consider a scenario in which anonymous, finite-state sensing devices are deployed in an ad-hoc communication network of arbitrary size and unknown topology, and explore what properties of the network graph can be stably computed by the devices. We show that they can detect whether the network has degree bounded by a constant d, and, if so, organize a computation that achieves asymptotically optimal linear memory use. We define a model of stabilizing inputs to such devices and show that a large class of predicates of the multiset of final input values are stably computable in any weakly-connected network. We also show that nondeterminism in the transition function does not increase the class of stably computable predicates.


Span Tree Network Graph Graph Property Directed Cycle Leader Election 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: PODC 2004: Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing, pp. 290–299. ACM Press, New York (2004)CrossRefGoogle Scholar
  2. 2.
    Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Urn automata. Technical Report YALEU/DCS/TR–1280, Yale University Department of Computer Science (2003)Google Scholar
  3. 3.
    Diamadi, Z., Fischer, M.J.: A simple game for the study of trust in distributed systems. Wuhan University Journal of Natural Sciences 6, 72–82 (2001); Also appears as Yale Technical Report TR–1207 (January 2001), available at CrossRefGoogle Scholar
  4. 4.
    Bernardinello, L., Cindio, F.D.: A survey of basic net models and modular net classes. In: Rozenberg, G. (ed.) APN 1992. LNCS, vol. 609, pp. 304–351. Springer, Heidelberg (1992)Google Scholar
  5. 5.
    Esparza, J., Nielsen, M.: Decibility issues for Petri nets - a survey. Journal of Informatik Processing and Cybernetics 30, 143–160 (1994)zbMATHGoogle Scholar
  6. 6.
    Esparza, J.: Decidability and complexity of Petri net problems-an introduction. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 374–428. Springer, Heidelberg (1998)Google Scholar
  7. 7.
    Mayr, E.W.: An algorithm for the general Petri net reachability problem. SIAM J. Comput. 13, 441–460 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Ginsburg, S., Spanier, E.H.: Semigroups, Presburger formulas, and languages. Pacific Journal of Mathematics 16, 285–296 (1966)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Hopcroft, J., Pansiot, J.: On the reachability problem for 5-dimensional vector addition systems. Theoretical Computer Science 8, 135–159 (1978)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Berry, G., Boudol, G.: The Chemical Abstract Machine. Theoretical Computer Science 96, 217–248 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ibarra, O.H., Dang, Z., Egecioglu, O.: Catalytic p systems, semilinear sets, and vector addition systems. Theor. Comput. Sci. 312, 379–399 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Brand, D., Zafiropulo, P.: On communicating finite-state machines. Journal of the ACM 30, 323–342 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Milner, R.: Bigraphical reactive systems: basic theory. Technical report, University of Cambridge, UCAM-CL-TR-523 (2001)Google Scholar
  14. 14.
    Intanagonwiwat, C., Govindan, R., Estrin, D.: Directed diffusion: a scalable and robust communication paradigm for sensor networks. In: Proceedings of the 6th Annual International Conference on Mobile computing and networking, pp. 56–67. ACM Press, New York (2000)CrossRefGoogle Scholar
  15. 15.
    Madden, S.R., Franklin, M.J., Hellerstein, J.M., Hong, W.: TAG: a Tiny AGgregation service for ad-hoc sensor networks. In: OSDI 2002: Fifth Symposium on Operating Systems Design and Implementation (December 2002)Google Scholar
  16. 16.
    Fang, Q., Zhao, F., Guibas, L.: Lightweight sensing and communication protocols for target enumeration and aggregation. In: Proceedings of the 4th ACM International Symposium on Mobile ad hoc networking & computing, pp. 165–176. ACM Press, New York (2003)CrossRefGoogle Scholar
  17. 17.
    Zhao, F., Liu, J., Liu, J., Guibas, L., Reich, J.: Collaborative signal and information processing: An information directed approach. Proceedings of the IEEE 91, 1199–1209 (2003)CrossRefGoogle Scholar
  18. 18.
    Grossglauser, M., Tse, D.N.C.: Mobility increases the capacity of ad hoc wireless networks. IEEE/ACM Transactions on Networking 10, 477–486 (2002)CrossRefGoogle Scholar
  19. 19.
    Kahn, J.M., Katz, R.H., Pister, K.S.J.: Next century challenges: mobile networking for “Smart Dust”. In: MobiCom 1999: Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking, pp. 271–278. ACM Press, New York (1999)CrossRefGoogle Scholar
  20. 20.
    Chatzigiannakis, I., Nikoletseas, S., Spirakis, P.: Smart dust protocols for local detection and propagation. In: POMC 2002: Proceedings of the second ACM international workshop on Principles of mobile computing, pp. 9–16. ACM Press, New York (2002)CrossRefGoogle Scholar
  21. 21.
    Itkis, G., Levin, L.A.: Fast and lean self-stabilizing asynchronous protocols. In: Proceeding of 35th Annual Symposium on Foundations of Computer Science, pp. 226–239. IEEE Press, Los Alamitos (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dana Angluin
    • 1
  • James Aspnes
    • 1
  • Melody Chan
    • 1
  • Michael J. Fischer
    • 1
  • Hong Jiang
    • 1
  • René Peralta
    • 1
  1. 1.Yale University 

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