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. It is assumed that nothing is known to the nodes of the network about the topology of the network, that is even the size of the network is not known, except that n>1 n > 1 . This lack of knowledge, about the value of n, is what distinguishes this setting from the vanilla model. For this setting, protocols for the vanilla model, may be executed with multiplicatively large estimates, say 2i 2 i in the ith phase, on the upper bound on the size of the network n . When the respective protocol with estimate 2i?n 2 i ? n on the size of the network is run, it will accomplish the task successfully. However, the problem that still remains is to determine when this process should terminate. Thus, to apply this design paradigm successful completion or incompletion of the process should be detected and this knowledge circulated in the network after appropriate number of rounds/phases of the protocol. In radio networks literature, this setting is known as the Acknowledged setting and broadcasting and gossiping problems for it are referred to as Acknowledged broadcasting and gossiping. An important feature of dynamic radio networks is that radio nodes can be dynamically introduced in the network from time to time and can be assigned labels in a much larger range, say polynomial in the size of the network, e.g. [1,,nc] [ 1 ,  , n c ] for some constant c. It is easy to see that protocols can be designed for the acknowledged setting only when the underlying communication network is strongly connected. We present the following results for these networks: (a) A deterministic protocol for Acknowledged broadcasting which takes NRG(n,nc) NRG ( n , n c ) rounds, where NRG(n,nc) NRG ( n , n c ) is the round complexity of deterministic gossiping for vanilla model. (b) A deterministic protocol for acknowledged gossiping, which takes O ( n 2 lg n ) rounds when collision detection mechanism is available. The schedule 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 sets of natural numbers which we call the 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 lg n ) rounds.
unknown radio networks acknowledged broadcasting and gossiping selecting-colliding families polynomially large labels