Efficient Communication in Unknown Networks

We consider the problem of disseminating messages in networks. We are interested in information dissemination algorithms in which machines operate independently without any knowledge of the network topology or size. Three communication tasks of increasing difficulty are studied. In blind broadcasting (BB) the goal is to communicate the source message to all nodes. In acknowledged blind broadcasting (ABB) the goal is to achieve BB and inform the source about it. Finally, in full synchronization (FS) all nodes must simultaneously enter the state terminated after receiving the source message. The algorithms should be efficient both in terms of the time required and the communication overhead they put on the network. We limit the latter by allowing every node to send a message to at most one neighbor in each round. We show that BB is achieved in time at most 2n in any n-node network and show networks in which time 2n-o(n) is needed. For ABB we show algorithms working in time (2+Ɛ)n, for any fixed positive constant Ɛ and sufficiently large n. Thus for both BB and ABB our algorithms are close to optimal. Finally, we show a simple algorithm for FS working in time 3n.The optimal time of full synchronization remains an open problem.

[1]  Rajeev Rastogi,et al.  Topology discovery in heterogeneous IP networks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[2]  Krzysztof Diks,et al.  Broadcasting in Unlabeled Tori , 1998, Parallel Process. Lett..

[3]  Wojciech Rytter,et al.  Deterministic broadcasting in unknown radio networks , 2000, SODA '00.

[4]  Gerard Tel,et al.  Introduction to Distributed Algorithms: Contents , 2000 .

[5]  Adrian Segall,et al.  Distributed network protocols , 1983, IEEE Trans. Inf. Theory.

[6]  Rüdiger Reischuk,et al.  Lower Bounds for Synchronous Networks and the Advantage of Local Information , 1987, WDAG.

[7]  Baruch Awerbuch,et al.  A trade-off between information and communication in broadcast protocols , 1990, JACM.

[8]  Krzysztof Diks,et al.  Broadcasting in Unlabeled Hypercubes with a Linear Number of Messages , 1998, Inf. Process. Lett..

[9]  Ramesh Govindan,et al.  Heuristics for Internet map discovery , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[10]  Mor Harchol-Balter,et al.  Resource discovery in distributed networks , 1999, PODC '99.

[11]  Juraj Hromkovič,et al.  Dissemination of Information in Interconnection Networks (Broadcasting & Gossiping) , 1996 .

[12]  Eli Upfal,et al.  Randomized Broadcast in Networks , 1990, Random Struct. Algorithms.

[13]  Krzysztof Diks,et al.  Perfect Broadcasting in Unlabeled Networks , 1998, Discret. Appl. Math..

[14]  Andrzej Pelc.  Fault‐tolerant broadcasting and gossiping in communication networks , 1996 .

[15]  Reuven Bar-Yehuda,et al.  On the time-complexity of broadcast in radio networks: an exponential gap between determinism randomization , 1987, PODC '87.

[16]  Arthur L. Liestman,et al.  A survey of gossiping and broadcasting in communication networks , 1988, Networks.