Abstract
Let G be a simple connected graph where every node is colored either black or white. Consider now the following repetitive process on G:eac h node recolors itself, at each local time step, with the color held by the majority of its neighbors. Since the clocks are not necessarily synchronized, the process can be asynchronous.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Z. Agur, A. S. Fraenkel, S. T. Klein. The number of fixed points of the majority rule. Discrete Mathematics, 70:295–302, 1988. 202
H. Attiya, J. van Leeuwen, N. Santoro, S. Zaks Efficient elections in chordal ring networks. Algorithmica, 4:437–446, 1989. 203
J.C. Bermond, J. Bond, D. Peleg, S. Perennes. Tight bounds on the size of 2-monopolies. In Proc. 3rd Colloquium on Structural Information and Communication Complexity, 170–179. 1996. 202
J.-C. Bermond, F. Comellas, D.F. Hsu. Distributed loop computer networks: a survey. Journal of Parallel and Distributed Computing, 24:2–10, 1995. 203
J.C. Bermond, D. Peleg. The power of small coalitions in graphs. In Proc. 2nd Coll. Structural Information and Communication Complexity, 173–184. 1995. 202
R. De Prisco, A. Monti, L. Pagli. Efficient testing and reconfiguration of VLSI linear arrays. Theoretical Computer Science, 197:171–188, 1998. 203
P. Flocchini, F. Geurts, N. Santoro. Optimal Dynamos in Chordal Rings. ULB, Dïpartement d’Informatique, Tech. Report 411, http://www.ulb.ac.be/di. 203
P. Flocchini, E. Lodi, F. Luccio, L. Pagli, N. Santoro. Irreversible dynamos in tori. Proc. EUROPAR 98, 554–562,1998. 203, 208
P. Flocchini, E. Lodi, F. Luccio, L. Pagli, N. Santoro. Monotone dynamos in tori. In Proc. 6th Coll. Struct. Information and Communication Complexity, 152–165, 1999. 203, 208
E. Goles, S. Martinez. Neural and Automata Networks, Dynamical Behavior and Applications. Kluwer Academic Publishers, 1990. 204
E. Goles, J. Olivos. Periodic behavior of generalized threshold functions. Discrete Mathematics, 30:187–189, 1980. 202
D. Krizanc, F.L. Luccio. Boolean routing on chordal rings. In Proc. 2nd Coll. Structural Information and Communication Complexity, 1995. 203
N. Linial, D. Peleg, Y. Rabinovich, M. Sachs. Sphere packing and local majority in graphs In Proc. 2nd ISTCS, 141–149, 1993. 202
F. Luccio, L. Pagli, H. Sanossian. Irreversible dynamos in butterflies. In Proc. 6th Coll. Structural Information and Communication Complexity, 204–218, 1999. 203
B. Mans. Optimal Distributed Algorithms in Unlabeled Tori and Chordal Rings. Journal on Parallel and Distributed Computing, 46(1): 80–90, 1997. 203
G. Moran. The r-majority vote action on 0-1 sequences. Discrete Mathematics, 132:145–174, 1994. 202
G. Moran. On the period-two-property of the majority operator in infinite graphs. Transactions of the American Mathematical Society, 347(5):1649–1667, 1995. 202
A. Nayak, N. Santoro, and R. Tan. Fault-tolerance of reconfigurable systolic arrays. In Proc. 20th Int’l Symp. Fault-Tolerant Computing, 202–209, 1990. 203
Yi Pan. A near-optimal multi-stage distributed algorithm for finding leaders in clustered chordal rings. Information Sciences, 76 (1-2):131–140, 1994. 203
D. Peleg. Local majority voting, small coalitions and controlling monopolies in graphs: A review. In Proc. 3rd Coll. Structural Information and Communication Complexity, 152–169, 1997. 202
D. Peleg. Size bounds for dynamic monopolies In Proc. 4th Coll. Structural Information and Communication Complexity, 151–161, 1997. 202, 203, 204
S. Poljak. Transformations on graphs and convexity. Complex Systems, 1:1021–1033, 1987. 202
N. Santoro, J. Ren, A. Nayak. On the complexity of testing for catastrophic faults. In Proc. 6th Int’l Symposium on Algorithms and Computation, 188–197, 1995. 203
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Flocchini, P., Geurts, F., Santoro, N. (1999). Optimal Irreversible Dy namos in Chordal Rings. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_21
Download citation
DOI: https://doi.org/10.1007/3-540-46784-X_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66731-5
Online ISBN: 978-3-540-46784-7
eBook Packages: Springer Book Archive