Abstract
This paper considers the problem of gossiping with packets of limited size in a network with cost function. We show that the problem of determining the minimum cost necessary to perform gossiping among a given set of participants with packets of limited size is NP-hard. We also give an approximate (with respect to the cost) gossiping algorithm. The ratio between the cost of an optimal algorithm and the approximate one is less than 1+2(k−1)/n, were n is the number of nodes participating to the gossiping process and k ≤ n−1 is the upper bound on the number of individual blocks of information that a packet can carry.
We also analyze the communication time and communication complexity, i.e., the product of the communication cost and time, of gossiping algorithms.
Research partially supported by the Italian Ministry of University and of Scientific Research in the framework of the “Algoritmi, Modelli di Calcolo e Strutture Informative” project.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. Bagchi, E.F. Schmeichel, and S.L. Hakimi, “Parallel Information Dissemination by Packets”, SIAM J. on Computing, 23 (1994), 355–372.
A. Bagchi, E.F. Schmeichel, and S.L. Hakimi, “Sequential Information Dissemination by Packets”, NETWORKS, 22 (1992), 317–333.
J.-C. Bermond, L. Gargano, A. Rescigno, and U. Vaccaro, “Fast Gossiping by Short Messages”, SIAM J. on Computing, to appear; an extended abstract appeared in: Proceedings of ICALP '95, Z. Fülöp and F. Gécseg (Eds.), Lectures Notes in Computer Science, vol. 944, pp. 135–146, Springer-Verlag, 1995.
J.-C. Bermond, S. Perennes, and T. Kodate, “Gossiping in Cayley Graphs by Packets”, in: Proceedings of the 8-th French-Japanese Conference on Combinatorics and Computer Science, Brest, July 1995.
D. P. Bertsekas, and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1989.
K. Diks, A. Pelc, “Efficient Gossiping by Packets in Networks with Random Faults”, SIAM J. Discrete Mathematics, 9 (1996).
S. Even and B. Monien, “On the number of Rounds Necessary to Disseminate Information”, Proc. 1st ACM Symp. on Parallel Algorithms and Architectures, Santa Fe, NM (1989), 318–327.
P. Fraignaud, E. Lazard, “Methods and Problems of Communication in Usual Networks”, Discrete Applied Math., 53 (1994), 79–134.
S. Fujita, “Gossiping in Mesh-Bus Computers by Packets with Bounded Length”, IPS Japan SIGAL, 36-6 (1993), 41–48.
L. Gargano, “Tighter Time Bounds on Fault-Tolerant Broadcasting and Gossiping”, NETWORKS, 22 (1992), 469–486.
L. Gargano and A. A. Rescigno, “Communication Complexity of Fault-Tolerant Information Diffusion”, Proceeding of the 5th IEEE Symposium on Parallel and Distributed Computing (SPDP 93), Dallas, TX, 564–571, 1993.
R.W. Haddad, S. Roy, and A. A. Schäffer, “On Gossiping with Faulty Telephone Lines”, SIAM J. on Alg. Discr. Meth., 8 (1987), 439–445.
S. Hedetniemi, S. Hedetniemi, and A. Liestman, “A Survey of Gossiping and Broadcasting in Communication Networks”, NETWORKS, 18 (1988), 129–134.
A. Hily and D. Sotteau, “Communications in Bus Networks”, in: Parallel and Distributed Computing, M. Cosnard, A. Ferreira, and J. Peters (Eds.), Lectures Notes in Computer Science, 805, Springer-Verlag, (1994), 197–206.
J. Hromkovič, R. Klasing, B. Monien, and R. Peine, “Dissemination of Information in Interconnection Networks (Broadcasting and Gossiping)”, in: F. Hsu, D.-Z. Du (Eds.) Combinatorial Network Theory, Kluwer Academic Publishers, (1995) 125–212.
W. Knödel, “New Gossips and Telephons”, Discrete Math., 30 (1980), 151–156.
D. W. Krumme, K.N. Venkataraman, and G. Cybenko, “Gossiping in Minimal Time”, SIAM J. on Computing, 21 (1992), 111–139.
A. Pelc, “Fault Tolerant Broadcasting and Gossiping in Communication Networks”, Technical Report (1995), University of Quebec.
R. Ravi, “Rapid Rumour Ramification: Approximating the Minimum Broadcasting Time”, Proc. 35th Annual Symposium on Foundations of Computer Science (FOCS '94), (1994), 202–213.
Q. Stout and B. Wagar, “Intensive Hypercube Communication”, J. Parallel and Distr. Computing, 10 (1990), 167–181.
O. Wolfson and A. Segall, “The Communication Complexity of Atomic Commitment and of Gossiping”, SIAM J. on Computing, 20 (1991), 423–450.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gargano, L., Rescigno, A.A., Vaccaro, U. (1996). Communication complexity of gossiping by packets. In: Karlsson, R., Lingas, A. (eds) Algorithm Theory — SWAT'96. SWAT 1996. Lecture Notes in Computer Science, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61422-2_135
Download citation
DOI: https://doi.org/10.1007/3-540-61422-2_135
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61422-7
Online ISBN: 978-3-540-68529-6
eBook Packages: Springer Book Archive