Efficient initialization algorithms on single-hop radio networks

We consider an initialization problem in single-hop radio networks. The initialization is the task of assigning distinct ID numbers to nodes in a network. We have greatly improved the previous results [10] for the initialization in an n-node network. We propose randomized initialization algorithms in two cases. The first case is that n is known to all the nodes and the second case is that n is unknown to all the nodes. The algorithm for the first case completes in en + Inn + O(1) expected time slots, and the algorithm for the second case completes in en + O( root n) expected slots. The main idea of the algorithm for the case that n is unknown is presumption of the number of nodes. In the algorithm, each node presumes the number of nodes efficiently and is assigned ID by using the algorithm for the case that n is known with the presumption value.