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On bootstrapping topology knowledge in anonymous networks

Published:09 February 2009Publication History
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Abstract

In this article, we quantify the amount of “practical” information (i.e., views obtained from the neighbors, colors attributed to the nodes and links) to obtain “theoretical” information (i.e., the local topology of the network up to distance k) in anonymous networks. In more detail, we show that a coloring at distance 2k + 1 is necessary and sufficient to obtain the local topology at distance k that includes outgoing links. This bound drops to 2k when outgoing links are not needed. A second contribution of this article deals with color bootstrapping (from which local topology can be obtained using the aforementioned mechanisms). On the negative side, we show that (i) with a distributed daemon, it is impossible to achieve deterministic color bootstrap, even if the whole network topology can be instantaneously obtained, and (ii) with a central daemon, it is impossible to achieve distance m when instantaneous topology knowledge is limited to m − 1. On the positive side, we show that (i) under the k-central daemon, deterministic self-stabilizing bootstrap of colors up to distance k is possible provided that k-local topology can be instantaneously obtained, and (ii) under the distributed daemon, probabilistic self-stabilizing bootstrap is possible for any range.

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                cover image ACM Transactions on Autonomous and Adaptive Systems
                ACM Transactions on Autonomous and Adaptive Systems  Volume 4, Issue 1
                January 2009
                213 pages
                ISSN:1556-4665
                EISSN:1556-4703
                DOI:10.1145/1462187
                Issue’s Table of Contents

                Copyright © 2009 ACM

                Publisher

                Association for Computing Machinery

                New York, NY, United States

                Publication History

                • Published: 9 February 2009
                • Revised: 1 September 2008
                • Accepted: 1 September 2008
                • Received: 1 March 2007
                Published in taas Volume 4, Issue 1

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