## Project Details

### Description

Rapid transfer of information is one of the single most important developments in technology that has led to our current global society. Like never before in history, computers and computer networks allow us to transfer nearly any form of information around the globe within second. However, with so many people plugged in to our information networks, it is more important than ever to maintain efficient and organized routing in these networks whose structure is constantly changing as users join and leave. Thus overlay network structures are required that can organize themselves into desirable states for routing information from the wide variety of states which could result from users joining and leaving at any time. Such self-stabilizing networks can automatically repair themselves from faults caused by sudden changes in the individual connections. These self-stabilizing mechanisms are not well understood, and theoretical results are needed to ensure that their usefulness can scale up to the exponentially increasing size and complexity of computers and networks of the future. We are requesting supplementary funds to an ongoing research project on selfstabilizing networks. Specifically, Phillip Stevens, the undergraduate would be assisting on analyzing the structure and routing algorithm for a self-stabilizing network which combines self-stabilizing linearization with classical de Bruijn routing to give a network which can change dynamically but which still maintains efficient routing between nodes. A classical de Bruijn graph provides very efficient routing while maintaining low node degree, and hence have been used in a wide scenario of applications: For example, some popular grid network topologies are de Bruijn graphs [1]; the Koorde protocol [2] for distributed hash tables uses a de Bruijn graph; in bioinformatics, de Bruijn graphs are used for de novo assembly of short read sequences into a genome [3]. However, the classical de Bruijn network is based on a static network, of fixed size and connections, which limits its use in many modern applications. By combining the routing ideas from the classical de Bruijn graph with self-stabilizing linearization, we hope to maintain the efficient routing of the de Bruijn graph but expand its usefulness to networks that are constantly changing in size and topology. 2 Specifically, we will show that the network maintains connectivity when a node leaves the system, and that there is a mechanism for estimating the size of the network (we assume that the nodes have no knowledge of the network topology, including the number of nodes in the system). Most importantly we will need to show that the expected routing time of the network is close to the classical de Bruijn graph, and that this time elapse occurs with high probability. With the help of the PI, Prof. Andrea Richa, the undergraduate will work on proving these results and any other required results that come up throughout the course of the research. Should the theoretical results prove promising, the undergraduate will also be able to begin design and construction of a simulation in order to verify experimentally the proven results and to better understand the actual implementation of such a network. The undergraduate has already been working on this project since January under some Arizona State University (ASU) undergraduate research seed funding and thus already has much of the necessary background required to perform these tasks. For additional biographical information and qualifications, see the supplementary biographical sketch and the justification of this supplement request.

Status | Finished |
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Effective start/end date | 9/1/08 → 8/31/12 |

### Funding

- National Science Foundation (NSF): $170,161.00

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