Abstract
The fundamental assumption in the classical theory of gossiping, broadcasting, and accumulation in networks is that atomic pieces of information are communicated in messages that consist of a set of such pieces. The communication mode in synchronous multiprocessor networks that are to compute a function does not fit this model. We show that, under certain assumptions about the way processors may communicate (“predictable reception”), computing an arbitrary n-ary function that has a “critical input” and distributing the result to all processors on an n-processor network takes at least as long as performing gossiping in the network graph. A similar relation exists between computing functions with the output appearing at only one processor and the complexity of broadcasting. Our methods can also be applied to extend known lower bounds for broadcasting a bit on EREW PRAMs to the much more general (randomized) distributed memory machines (DMMs).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
P. Beame, M. Kutyłowski, and M. Kik, Information Broadcasting by exclusive-read PRAMs, Parallel Processing Letters 1 & 2 (1994) 159–169.
G. Belting, Untere Schranken für die Berechnung von Booleschen Funktionen in vollständigen Prozessornetzwerken im Telefon-und Telegraf-Modus, Diplomarbeit, Universität-Gesamthochschule-Paderborn, Paderborn, 1994.
S. Cook, C. Dwork, and R. Reischuk, Upper and lower time bounds for parallel random access machines without simultaneous writes, SIAM J. Comput. 15 (1986) 87–97.
M. Dietzfelbinger, Gossiping and broadcasting versus computing functions in networks, ECCC (http://www.eccc.uni-trier.de/eccc/), Report TR96-052, 1996.
M. Dietzfelbinger, M. Kutyłowski, and R. Reischuk, Exact time bounds for computing Boolean functions on PRAMs without simultaneous writes, in: Proc. 2nd Annual ACM Symp. on Parallel Algorithms and Architectures, 1990, pp. 125–135.
M. Dietzfelbinger, M. Kutyłowski, and R. Reischuk, Exact lower bounds for computing Boolean functions on CREW PRAMs, J. Comput. Syst. Sci. 48 (1994) 1231–254.
M. Dietzfelbinger and F. Meyer auf der Heide, Simple, efficient shared memory simulations, in: Proc. 5th ACM Symp. on Parallel Algorithms and Architectures, 1993, pp. 110–118.
S. Even and B. Monien, On the number of rounds necessary to disseminate information, in: Proc. ACM Symp. on Parallel Algorithms and Architectures, 1989, pp. 318–327.
F. Fich, The complexity of computation on the parallel random access machine, in J. H. Reif (ed.), Synthesis of Parallel Computation, Morgan Kaufmann, San Mateo, 1994, pp. 843–899.
P. Fraigniaud and E. Lazard, Methods and problems of communication in usual networks, Discrete Applied Math. 53 (1994) 79–134.
L. A. Goldberg, M. Jerrum, T. Leighton, and S. Rao, A doubly logarithmic communication algorithm for the completely connected optical communication parallel computer, in: Proc. 5th Annual ACM Symp. on Parallel Algorithms and Architectures, 1993, pp. 300–309.
L. A. Goldberg, Y. Matias, and S. Rao, An optical simulation of shared memory, in: Proc. 6th Annual ACM Symp. on Parallel Algorithms and Architectures, 1994, pp. 257–267.
S. M. Hedetniemi, S. T. Hedetniemi, and A. L. Liestman, A survey of gossiping and broadcasting in communication networks, Networks 18 (1986) 319–349.
I. Höltring, Broadcast und Gossip in parallelen Netzwerken, Diplomarbeit, Universität-Gesamthochschule-Paderborn, Paderborn, 1994.
J. Hromkovič, C.-D. Jeschke, and B. Monien, Optimal algorithms for dissemination of information in some interconnection networks, Algorithmica 10 (1993) 24–40.
J. Hromkovič, R. Klasing, B. Monien, and R. Peine, Dissemination of information in interconnection networks (broadcasting & gossiping), in: D.-Z. Du and D. F. Hsu (eds.), Combinatorial Network Theory, Kluwer Academic Publishers, Amsterdam, 1996, pp. 125–212.
R. M. Karp and V. Ramachandran, Parallel algorithms for shared-memory machines, in J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Vol. A, Algorithms and Complexity, Elsevier, Amsterdam, 1990, pp. 869–941.
D. W. Krumme, G. Cybenko, and K. N. Venkatamaran, Gossiping in minimal time, SIAM J. Comput. 21 (1992) 111–139.
R. Labahn and I. Warnke, Quick gossiping by multi-telegraphs, in: R. Bodendiek and R. Henn (eds.), Topics in Combinatorics and Graph Theory, Physica-Verlag, Heidelberg, 1990, pp. 451–458.
F. Meyer auf der Heide, C. Scheideler, and V. Stemann, Exploiting storage redundancy to speed up randomized shared memory simulations, in: E. W. Mayr and C. Puech (eds.), Proc. 12th Annual Symposium on Theoretical Aspects of Computer Science (STACS 95), Lecture Notes in Computer Science 900, Springer, Berlin, 1995, pp. 267–278.
D. Richards and A. L. Liestman, Generalizations of broadcasting and gossiping, Networks 18 (1988) 125–138.
V. S. Sunderam and P. Winkler, Fast information sharing in a complete network, Discrete Applied Math. 42 (1991) 75–86.
G. Tel, Introduction to Distributed Algorithms, Cambridge University Press, Cambridge, 1994.
U. Vishkin and A. Wigderson, Trade-offs between depth and width in parallel computation, SIAM J. Comput. 14 (1985) 303–314.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dietzfelbinger, M. (1997). Gossiping and broadcasting versus computing functions in networks. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023459
Download citation
DOI: https://doi.org/10.1007/BFb0023459
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62616-9
Online ISBN: 978-3-540-68342-1
eBook Packages: Springer Book Archive