On ?-Alert Problem

In this paper we introduce and analyse the λ-Alert problem: in a single hop radio network a subset of stations is activated. The aim of the protocol is to decide if the number of activated stations is greater or equal to λ. This problem is similar to the k-Selection problem. It can also be seen as an extension of the standard Alert problem. In our paper we consider the λ-Alert problem in various settings. We describe characteristics of oblivious and adaptive deterministic algorithms for the model with and without collision detection. We also show some results for randomized algorithms. In particular, we present a very efficient Las Vegastype algorithm which is immune to an adversary.