Information dissemination in unknown radio networks with large labels

We consider the problems of deterministic broadcasting and gossiping in completely unknown ad-hoc radio networks. We assume that nothing is known to the nodes about the topology or even the size of the network, n, except that n > 1. Protocols for vanilla model, when n is known, may be run for increasingly larger estimates 2 on the size of the network, but one cannot determine when such a protocol should terminate. Thus, to carry this design paradigm, successfull completion or incompletion of the process should be detected, and this knowledge circulated in the network. In radio networks litertaure, this setting is referred to as Acknowledged broadcasting and gossiping. An important feature of dynamic ad-hoc radio networks is that radio nodes become ineffective due to a variety of reasons and new nodes are introduced from time-to-time. Thus, the new nodes have to assigned labels in a much larger range, say polynomial in the size of the network, e.g., [1, . . . , n], for some constant c. For the above setting, we present the following results for strongly connected networks: (a) A deterministic protocol for acknowledged broadcasting which takes NRG(n, n) rounds, where NRG(n, n) is the round complexity of deterministic gossiping for vanilla model. (b) A deterministic protocol for acknowledged gossiping, which takes O(n lg n) rounds when collision detection mechanism is available. The structure of the transmissions of nodes in the network, to enable them to infer collisions, and discover existence of unknown in-neighborhood as a result, is abstracted as a family of integral sets called Selecting-Colliding family. We prove the existence of Selecting-Colliding families using the probabilistic method and employ them to design protocol for acknowledged gossiping when no collision detection mechanism is available. Finally, we present a deterministic protocol for acknowledged broadcasting for bidirectional networks, with a round complexity of O(n lgn) rounds.