Neighborhood Communications in Networks

Broadcasting (resp. gossiping) refers to the task whereby a node (resp. every node) in a network, knowing a piece of information, must transmit it to all the other nodes. We consider here a generalized form of broadcasting and gossiping, that we call respectively k-neighborhood broadcasting and k-neighborhood gossiping (k-NB and k-NG, for short). It consists in the following : a node u (resp. every node u) in the network has to send its information to all the nodes which are at distance less than or equal to k from u. We study fe-NB and fe-NG in paths, trees, cycles, 2-dimensional grids and 2-dimensional tori under the store-and-forward, 1-port, unit cost model. For most of these families, we give the optimal k-NB (resp. fe-NG) time; if not, the optimal k-NB (resp. k-NG) time is given within an additive (resp. multiplicative) constant never exceeding 2.