Optimal gathering algorithms in multi-hop radio tree networks with interferences.

International audienceWe study the problem of gathering information from the nodes of a multi-hop radio network into a pre-defined destination node under the interference constraints. In such a network, a message can only be properly received if there is no interference from another message being simultaneously transmitted. The network is modeled as a graph, where the vertices represent the nodes and the edges, the possible com- munications. The interference constraint is modeled by a fixed integer dI ? 1, which implies that nodes within distance d I in the graph from one sender cannot receive messages from another node. In this paper, we suppose that it takes one unit of time (slot) to transmit a unit-length message. A step (or round) consists of a set of non interfering (compat- ible) calls and uses one slot. We present optimal algorithms that give minimum number of steps (delay) for the gathering problem with buffer- ing possibility, when the network is a tree, the root is the destination and dI = 1. In fact we study the equivalent personalized broadcasting problem instead