Optimal Gathering in Radio Grids with Interference

Jean-Claude Bermond 1 Joseph Peters 2
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : We study the problem of gathering information from the nodes of a radio network into a central node. We model the network of possible transmissions by a graph and consider a binary model of interference in which two transmissions interfere if the distance in the graph from the sender of one transmission to the receiver of the other is $d_I$ or less. A {\em round} is a set of non-interfering transmissions. In this paper, we determine the exact number of rounds required to gather one piece of information from each node of a square two-dimensional grid into the central node. If $d_I = 2k-1$ is odd, then the number of rounds is $k(N-1)-c_k$ where $N$ is the number of nodes and $c_k$ is a constant that depends on $k$. If $d_I = 2k$ is even, then the number of rounds is $(k+\frac{1}{4})(N-1)-c'_k$ where $c'_k$ is a constant that depends on $k$. The even case uses a method based on linear programming duality to prove the lower bound, and sophisticated algorithms using the symmetry of the grid and non-shortest paths to establish the matching upper bound. We then generalize our results to hexagonal grids.
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Jean-Claude Bermond, Joseph Peters. Optimal Gathering in Radio Grids with Interference. 2011. 〈inria-00610038〉

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