An optimal algorithm of acknowledged broadcasting in ad hoc radio networks

We consider the problem of distributed deterministic broadcasting in synchronous radio networks whose topology and size are unknown. Radio networks can be modeled by directed graphs. It has been shown that there does not exist any algorithm of acknowledged radio broadcasting(ARB) on the model without a collision detection even if graphs are restricted to symmetric ones, where ARB is a broadcasting task in which a distinguished node(called source) transmits a source message to all nodes and it confirms that all nodes have received the source message. In this paper, on the model of radio networks with a collision detection, we show an O(r + ecc) time deterministic ARB algorithm for symmetric graphs, where r is the length of the source message and ecc is the largest distance from the source to any other node.