Gathering Radio Messages in the Path

In this paper, we address the problem of gathering information in one node (sink) of a radio network where interference constraints are present: when a node transmits, it produces interference in an area bigger than the area in which its message can actually be received. The network is modeled by a graph; a node is able to transmit one unit of information to the set of vertices at distance at most dT in the graph, but when doing so it generates interferences that do not allow nodes at distance up to dI (dI ≥ dT ) to listen to other transmissions. We are interested in finding a gathering protocol, that is an ordered sequence of rounds (each round consists of non-interfering simultaneous transmissions) such that w(u) messages are transmitted from node u to a fixed node called the sink. Our aim is to find the minimum number of rounds called gathering time. In this article, we focus on the specific case where the network is a path and where the traffic is unitary (w(u) = 1 for all u); indeed this simple case appears to be already very difficult. We give for arbitrary location of the sink lower and upper bounds on the number of rounds that differ only by a constant independent of the length of the path. When the sink is an end-vertex of the path, we present a method to construct incremental protocols. An incremental protocol for the path on n+1 vertices is obtained from a protocol for n vertices by adding new rounds and new calls to some rounds but without changing the calls of the original rounds. We conjecture that this incremental construction gives optimal protocols and prove it in some special cases (dT prime in particular).