2 research outputs found
On The Termination of a Flooding Process
Flooding is among the simplest and most fundamental of all distributed
network algorithms. A node begins the process by sending a message to all its
neighbours and the neighbours, in the next round forward the message to all the
neighbours they did not receive the message from and so on. We assume that the
nodes do not keep a record of the flooding event. We call this amnesiac
flooding (AF). Since the node forgets, if the message is received again in
subsequent rounds, it will be forwarded again raising the possibility that the
message may be circulated infinitely even on a finite graph. As far as we know,
the question of termination for such a flooding process has not been settled -
rather, non-termination is implicitly assumed.
In this paper, we show that synchronous AF always terminates on any arbitrary
finite graph and derive exact termination times which differ sharply in
bipartite and non-bipartite graphs. Let be a finite connected graph. We
show that synchronous AF from a single source node terminates on in
rounds, where is the eccentricity of the source node, if and only if is
bipartite. For non-bipartite , synchronous AF from a single source
terminates in rounds where and is the diameter of
. This limits termination time to at most and at most for
bipartite and non-bipartite graphs respectively. If communication/broadcast to
all nodes is the motivation, our results show that AF is asymptotically time
optimal and obviates the need for construction and maintenance of spanning
structures like spanning trees. The clear separation in the termination times
of bipartite and non-bipartite graphs also suggests mechanisms for distributed
discovery of the topology/distances in arbitrary graphs.
For comparison, we show that, in asynchronous networks, an adaptive adversary
can force AF to be non-terminating.Comment: A summary to appear as a Brief Announcement at ACM PODC'19. Full
version under submissio