Deterministic communication in radio networks with large labels

We study deterministic gossiping in ad-hoc radio networks, where labels of the nodes are large, i.e., they are polynomially large in the size n of the network. A label-free model was introduced in the context of randomized broadcasting in ad-hoc radio networks, see [2]. Most of the work on deterministic communication in ad-hoc networks was done for the model with labels of size O(n), with few exceptions; Peleg [19] raised the problem of deterministic communication in ad-hoc radio networks with large labels and proposed the first deterministic O(n² logn)-time broadcasting algorithm. In [11] Chrobak et al. proved that deterministic radio broadcasting can be performed in time O(n log² n); their result holds for large labels. Here we propose two new deterministic gossiping algorithms for ad-hoc radio networks with large labels. In particular: - a communication procedure giving an O(n^5/3 log³ n)-time deterministic gossiping algorithm for directed networks and an O(n^4/3 log³ n)-time algorithm for undirected networks; -a gossiping procedure designed particularly for undirected networks resulting in an almost linear O(n log³ n)-time algorithm.