# Robust Topology Control Protocols

## Abstract

Topology control protocols attempt to reduce the energy consumption of nodes in an ad-hoc wireless network while maintaining sufficient network connectivity. Topology control protocols with various features have been proposed, but they all lack robustness and are extremely sensitive to faulty information from neighbors. For example, the XTC protocol (R. Wattenhofer and A. Zollinger, XTC: A practical topology control algorithm for ad-hoc networks, *WMAN 2004*) can be forced to construct a disconnected network even if two nodes in the network receive slightly faulty distance information from one neighbor each. A key step in most localized topology control protocols is one in which each node establishes a total ordering on its set of neighbors based on information received from them. In this paper, we propose a metric for *robustness* of localized topology control protocols and define an *r*-robust topology control protocol as one that returns a correct output network even when its neighborhood orderings have been modified by up to *r*–1 adjacent swaps by a malicious adversary. We then modify XTC in a simple manner to derive a family of *r*-robust protocols for any *r* > 1. The price we pay for increased robustness is in terms of decreased network sparsity; however we can bound this decrease and we show that in transforming XTC from a 1-robust protocol (which it trivially is) into an *r*-robust protocol, the maximum vertex degree of the output network increases by a factor of \(O(\sqrt{r})\). An extremely pleasant side-effect of our design is that the output network is both \(\Omega(\sqrt{r})\)-edge connected and \(\Omega(\sqrt{r})\)-vertex connected provided the input network is. Thus ensuring robustness of the protocol seems to give fault-tolerance of the output for free. Our *r*-robust version of XTC is almost as simple and practical as XTC and like XTC it only involves 2 rounds of communication between a node and its neighbors.

## Keywords

Ad-hoc wireless networks fault-tolerance*k*-connectivity robustness topology control protocols

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.Bahramgiri, M., Hajiaghayi, M., Mirrokni, V.S.: Fault-tolerant and 3-dimensional distributed topology control algorithms in wireless multi-hop networks. In: Proceedings of the 11th IEEE International Conference on Computer Communications and Networks (IC3N), pp. 392–398 (2002)Google Scholar
- 2.Burkhart, M., von Rickenbach, P., Wattenhofer, R., Zollinger, A.: Does topology control reduce interference? In: Proceedings of the 4th ACM International Symposium on Mobile Ad-Hoc Networking and Computing, MOBIHOC (2003)Google Scholar
- 3.Kuhn, F., Wattenhofer, R., Zhang, Y., Zollinger, A.: Geometric ad-hoc routing: of theory and practice. In: Proceedings of the 22nd ACM Symposium on the Principles of Distributed Computing, PODC (2003)Google Scholar
- 4.Kuhn, F., Wattenhofer, R., Zollinger, A.: Ad-hoc networks beyond unit disk graphs. In: DIAL-POMC 2003 (2003)Google Scholar
- 5.Li, L., Halpern, J., Bahl, P., Wang, Y., Wattenhofer, R.: Analysis of a cone-based distributed topology control algorithm for wireless multi-hop networks. In: Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC), pp. 264–273 (2001)Google Scholar
- 6.Li, N., Hou, J.C.: FLSS: A fault-tolerant topology control algorithm for wireless networks. In: Proceedings of MOBICOM (2004)Google Scholar
- 7.Moore, D., Leonard, J., Rus, D., Teller, S.: Robust distributed network localization with noisy range measurements. In: SenSys 2004 (2004)Google Scholar
- 8.Moscibroda, T., O’Dell, R., Wattenhofer, M., Wattenhofer, R.: Virtual coordinates for ad hoc and sensor networks. In: DIAL-POMC 2004 (2004)Google Scholar
- 9.Prakash, R.: Unidirectional links prove costly in wireless ad-hoc networks. In: Proceedings of the 3rd International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communication, DIAL-M (1999)Google Scholar
- 10.Wang, Y., Li, X.Y.: Localized construction of bounded degree planar spanner for wireless ad hoc networks. In: Proceedings of the 2003 Joint Workshop on Foundations of Mobile Computing, pp. 59–68 (2003)Google Scholar
- 11.Wattenhofer, R., Zollinger, A.: XTC: A practical topology control algorithm for ad-hoc networks. In: Proceedings of the 4th International Workshop on Algorithms for Wireless, Mobile, Ad Hoc and Sensor Networks, WMAN 2004 (2004)Google Scholar