Algorithms and Lp-duality Based Lower Bounds in Ad-hoc Radio Networks by Rohan Jude Fernandes

OF THE DISSERTATION Algorithms and LP-Duality Based Lower Bounds in Ad-hoc Radio Networks by Rohan Jude Fernandes Dissertation Director: Mart́ın Farach-Colton An Ad-hoc Radio Network consists of nodes with no knowledge of its neighbors and knowledge of its own ID and n, the size of the network. In this thesis, we present algorithms and lower bounds related to ad-hoc network initialization. Sensor networks are an important type of ad-hoc Radio Network, consisting of sensor nodes very weak computers. Usually sensor nodes get distributed at random on a surface where they must wake up and initialize into a Radio Network. Due to the strict restrictions on sensor node capabilities, it is difficult to find efficient solutions to even basic problems. In our first result, we present a formal Weak Sensor Model that summarizes the literature on sensor node restrictions, taking the most restrictive choices when possible. We show that sensor connectivity graphs have low-degree subgraphs with good hopstretch, as required by the Weak Sensor Model. We then give a Weak Sensor Model-compatible protocol for finding such graphs that runs in O(log n) time with high probability. We then present new lower bounds for collision-free transmissions in Radio Networks. Our main result is a tight lower bound of Ω(log n log(1/ )) on the -failureprobability time required by a fair randomized protocol to achieve a clear transmission in a one-hop network. We also prove a new lower bound for the important multi-hop