This Article 
 Bibliographic References 
 Add to: 
Computing on Anonymous Networks: Part II-Decision and Membership Problems
January 1996 (vol. 7 no. 1)
pp. 90-96

Abstract—In anonymous networks, the processors do not have identity numbers. In Part I of this paper, we characterized the classes of networks on which some representative distributed computation problems are solvable under different conditions. A new graph property called symmetricity played a central role in our analysis of anonymous networks. In Part II, we turn our attention to the computational complexity issues. We first discuss the complexity of determining the symmetricity of a given graph, and then that of testing membership in each of the 16 classes of anonymous networks defined in Part I. It turns out that, depending on the class, the complexity varies from P-time to NP-complete or co-NP-complete.

[1] A.V. Aho,J.E. Hopcroft, and J.D. Ullman,The Design and Analysis of Computer Algorithms.Reading, Mass.: Addison-Wesley, 1974.
[2] D. Angluin, “Global and Local Properties in Networks of Processors,” Proc. 12th ACM Symp. Theory of Computing, pp. 82–93, 1980.
[3] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness.New York: W.H. Freeman, 1979.
[4] A.F. Harary,Graph Theory.Reading, Mass.: Addison-Wesley, 1969.
[5] S. Micali and V.V. Vazirani,"An$O\!\left( {\sqrt {\left| V \right|}\times \left| E \right|} \right)$algorithm for finding maximum matching in general graphs," Proc. 21st IEEE Symp. Foundations of Computer Science, pp. 17-27,Syracuse, N.Y., 1980.
[6] J. Petersen,"Die Theorie der regulären Graphs," Acta Mathematica, vol. 15, pp. 193-220, 1891.
[7] M. Yamashita and T. Kameda, “Computing on Anonymous Networks,” Proc. Seventh ACM Symp. Principles Distributed Computing, Toronto, pp. 117–131, 1988.
[8] M. Yamashita and T. Kameda, “Computing on Anonymous Networks, Part I: Characterizing the Solvable Cases,” IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 1, pp. 69–89, Jan. 1996.

Index Terms:
Anonymous network, computability, distributed computing, leader election, edge election, spanning tree construction, topology recognition, NP-completeness.
Masafumi Yamashita, Tsunehiko Kameda, "Computing on Anonymous Networks: Part II-Decision and Membership Problems," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 1, pp. 90-96, Jan. 1996, doi:10.1109/71.481600
Usage of this product signifies your acceptance of the Terms of Use.