### DIMACS Theoretical Computer Science Seminar

Title: Upper and Lower Bounds in Sensor Network Bootstrapping

Speaker: Rohan Fernandes, Rutgers University

Date: November 29, 2005 2:00-3:00pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Sensor nodes are very weak computers that get distributed at random on a surface. Once deployed, they must wake up and form a radio network. Sensor network bootstrapping research thus has three parts: one must model the restrictions on sensor nodes; one must prove that the connectivity graph of the sensors has a subgraph that would make a good network; and one must give a distributed protocol for finding such a network subgraph that can be implemented on sensor nodes.

Although many particular restrictions on sensor nodes are implicit or explicit in many papers, there remain many inconsistencies and ambiguities from paper to paper. The lack of a clear model means that solutions to the network-bootstrapping problem in both the theory and systems literature all violate constraints on sensor nodes. For example, random geometric graph results on sensor networks predict the existence of subgraphs on the connectivity graph with good route-stretch, but these results do not address the degree of such a graph, and sensor networks must have constant degree. Furthermore, proposed protocols for actually finding such graphs require that nodes have too much memory, whereas others assume the existence of a contention-resolution mechanism.

We present a formal Weak Sensor Model(WSM) 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 \emph{hop-stretch}, as required by the WSM. Finally, we give a WSM-compatible protocol for finding such graphs. Ours is the first network initialization algorithm that is implementable on sensor nodes.

Time allowing, we will also show new lower bounds for collision-free transmissions in Radio Networks. Our main result is a tight lower bound of $\Omega(\log n \log (1/\epsilon))$ on the time required by a uniform randomized protocol to achieve a clear transmission with success probability $1-\epsilon$ in a one-hop setting. This result is extended to non-uniform protocols as well. A new lower bound is proved for the important multi-hop setting of nodes distributed as a connected Random Geometric Graph. Our main result is tight for a variety of problems.