Abstract
We consider broadcasting among n processors, f of which can be faulty. A fault-free processor, called the source, holds a piece of information which has to be transmitted to all other fault-free processors. We assume that the fraction f /n of faulty processors is bounded by a constant ,γ < 1. Transmissions are fault free. Faults are assumed of crash, type: faulty processors do not send or receive messages. We use the whispering model: pairs of processors communicating in one round must form a matching. A fault-free processor sending a message to an other processor becomes aware of whether this processor is faulty or fault free and can adapt future transmissions accordingly. The main result of the paper is a broadcasting algorithm working in O(log n) rounds and using O(n) messages of logarithmic size, in the worst case. This is an improvement of the result from [10] where O((log n)2) rounds were used. Our method also gives the first algorithm for adaptive distributed fault diagnosis in O (log n) rounds.
This work was done during the author's stay at the Université du Québec à Hull.
Research supported in part by NSERC grant OGP 0008136.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. Bagchi and S.L. Hakimi, Information dissemination in distributed systems with faulty units, IEEE Trans. Comp. 43 (1994), 698–710.
R. Beigel, W. Hurwood and N. Kahale, Fault diagnosis in a flash, Proc. 36th Symp. on Found. of Comp. Sci. (1995), 571–580.
K.A. Berman and M. Hawrylycz, Telephone problems with failures, SIAM J. Alg. Disc. Meth. 7 (1986), 13–17.
D.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, (1989).
B.S. Chlebus, L. Gasieniec and A. Pelc, Fast deterministic simulation of computations on faulty parallel machines, Proc. 3rd Ann. Eur. Symp. on Alg. ESA'95, (1995), 89–101.
A.T. Dahbura, System-level diagnosis: A perspective for the third decade, Concurrent Computation: Algorithms, Architectures, Technologies, Plenum Press, New York (1988).
A. Farley, Reliable minimum-time broadcast networks, in: Proc. 18th SE Conf. on Combinatorics, Graph Theory and Computing, Congressus Numerantium 59 (1987), 37–48.
P. Fraigniaud and E. Lazaxd, Methods and problems of communication in usual networks, Disc. Appl. Math. 53 (1994), 79–133.
L. Gaxgano and U. Vaccaxo, Minimum time networks tolerating a logarithmic number of faults, SIAM J. Disc. Math. 5 (1992), 178–198.
L. Gasieniec and A. Pelc, Adaptive broadcasting with faulty nodes, Parallel Computing 22 (1996), 903–912.
L. Gasieniec and A. Pelc, Broadcasting with linearly bounded transmission faults, Discrete Applied Mathematics, to appear.
S.M. Hedetniemi, S.T. Hedetniemi and A.L. Liestman, A survey of gossiping and broadcasting in communication networks, Networks 18 (1988), 319–349.
S.L. Johnsson and C.T. Ho, Matrix multiplication on Boolean cubes using generic communication primitives, in: Parallel Processing and Medium-Scale Multiprocessors, A. Wouk (Ed.), SIAM, (1989), 108–156.
J.G. Kuhl and S.M. Reddy, Distributed fault-tolerance for large multiprocessor systems, Proc. IEEE Symp. Comp. Architecture (1980), 23–30.
A. Lubotzky, R. Philips and P. Sasnak, Explicit expanders and the Ramanujan conjectures, Proc. 18th Ann. ACM Symp. on Theory of Computing (1986), 247–263.
K. Nakajima, A new approach to system diagnosis, Proc. 19th Allerton Conf. Commun. Contr. and Computing (1981), 697–706.
A. Pelc, Fault-tolerant broadcasting and gossiping in communication networks, Networks 28 (1996), 143–156.
D. Peleg and A.A. Schiffer, Time bounds on fault-tolerant broadcasting, Networks 19 (1989), 803–822.
F. Preparata, G. Metze and R. Chien, On the connection assignment problem of diagnosable systems, IEEE Transactions on Electron. Computers 16 (1967), 848–854.
E. Upfal, Tolerating a linear number of faults in networks of bounded degree, Information and Computation 115 (1994), 312–320.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Diks, K., Pelc, A. (1997). Optimal adaptive broadcasting with a bounded fraction of faulty nodes. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_10
Download citation
DOI: https://doi.org/10.1007/3-540-63397-9_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63397-6
Online ISBN: 978-3-540-69536-3
eBook Packages: Springer Book Archive