Abstract
A new communication mode for the dissemination of information among processors of interconnection networks via vertex-disjoint paths is introduced and investigated. In this communication mode, in one communication step two processors communicating via a path P send their pieces of information to all other processors on this path, too. The complexity of a communication algorithm is measured by the number of communication steps (rounds).
The main results are optimal (or nearly optimal, up to one round) broadcast, accumulation, and gossip algorithms for paths, cycles, complete graphs, two-dimensional grids, hypercubes and hypercube-like networks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bollobas, B.: Graph Theory. Springer, New York (1979)
Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (1990)
Even, S.: Graph Algorithms. Pitman, London (1979)
Farley, A.M.: Minimum-Time Line Broadcast Networks. Networks 10, 5970 (1980)
Feldmann, R., Hromkovič, J., Madhavapeddy, S., Monien, B., Mysliwietz, P.: Optimal Algorithms for Dissemination of Information in Generalized Communication Modes. Discrete Applied Mathematics 53(1-3), 55–78 (1994)
Fraigniaud, P., Lazard, E.: Methods and problems of communication in usual networks. Discrete Applied Mathematics 53(1-3), 79–133 (1994)
Feldmann, R., Mysliwietz, P.: The Shuffle Exchange Network has a Hamiltonian Path. Mathematical Systems Theory 29(5), 471–485 (1996)
Hedetniemi, S.M., Hedetniemi, S.T., Liestman, A.L.: A Survey of Gossiping and Broadcasting in Communication Networks. Networks 18, 319–349 (1988)
Hromkovič, J., Klasing, R., Monien, B., Peine, R.: Dissemination of Information in Interconnection Networks (Broadcasting and Gossiping). In: Du, D.-Z., Hsu, F. (eds.) Combinatorial Network Theory, pp. 125–212. Kluwer Academic Publishers, Dordrecht (1995)
Hromkovič, J., Klasing, R., Stöhr, E.A.: Dissemination of Information in Vertex-Disjoint Paths Mode. Computers and Artificial Intelligence 15(4), 295–318 (1996)
Hromkovič, J., Klasing, R., Stöhr, E.A., Wagener, H.: Gossiping in Vertex-Disjoint Paths Mode in d-Dimensional Grids and Planar Graphs. Information and Computation 123(1), 17–28 (1995)
Hromkovič, J., Klasing, R., Unger, W., Wagener, H.: Optimal Algorithms for Broadcast and Gossip in the Edge-Disjoint Path Modes. Information and Computation 133(1), 1–33 (1997)
Hromkovič, J., Loryś, K., Kanarek, P., Klasing, R., Unger, W., Wagener, H.: On the Sizes of Permutation Networks and Consequences for Efficient Simulation of Hy-percube Algorithms on Bounded-Degree Networks. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 255–266. Springer, Heidelberg (1995)
Klasing, R.: On the Complexity of Broadcast and Gossip in Different Communication Modes (Dissertation). Shaker Verlag, Aachen (1996)
Klasing, R.: The Relationship Between Gossiping in Vertex-Disjoint Paths Mode and Bisection Width. Discrete Applied Mathematics 82(1-3), 227–244 (1998)
Leighton, F.T.: Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann Publishers, San Francisco (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Böckenhauer, HJ. (1998). Communication in the Two-Way Listen-in Vertex-Disjoint Paths Mode. In: Hromkovič, J., Sýkora, O. (eds) Graph-Theoretic Concepts in Computer Science. WG 1998. Lecture Notes in Computer Science, vol 1517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10692760_4
Download citation
DOI: https://doi.org/10.1007/10692760_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65195-6
Online ISBN: 978-3-540-49494-2
eBook Packages: Springer Book Archive