Abstract
We present a distributed asynchronous algorithm that, for every undirected weighted n-node graph G, constructs name-independent routing tables for G. The size of each table is \(\tilde{O}(\sqrt{n}\,)\), whereas the length of any route is stretched by a factor of at most 7 w.r.t. the shortest path. At any step, the memory space of each node is \(\tilde{O}(\sqrt{n}\,)\). The algorithm terminates in time O(D), where D is the hop-diameter of G. In synchronous scenarios and with uniform weights, it consumes \(\tilde{O}(m\sqrt{n} + n^{3/2}\) min\({D,\sqrt{n}\,})\) messages, where m is the number of edges of G.
In the realistic case of sparse networks of poly-logarithmic diameter, the communication complexity of our scheme, that is \(\tilde{O}(n^{3/2})\), improves by a factor of \(\sqrt{n}\) the communication complexity of any shortest-path routing scheme on the same family of networks. This factor is provable thanks to a new lower bound of independent interest.
All the authors are supported by the ANR-project DISPLEXITY (ANR-11-BS02-014), and the European STREP7-project EULER. The first author is also member of the “Institut Universitaire de France”.
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Gavoille, C., Glacet, C., Hanusse, N., Ilcinkas, D. (2013). On the Communication Complexity of Distributed Name-Independent Routing Schemes. In: Afek, Y. (eds) Distributed Computing. DISC 2013. Lecture Notes in Computer Science, vol 8205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41527-2_29
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