# Bounding the locality of distributed routing algorithms

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## Abstract

We examine bounds on the locality of routing. A local routing algorithm makes a sequence of distributed forwarding decisions, each of which is made using only local information. Specifically, in addition to knowing the node for which a message is destined, an intermediate node might also know (1) its local neighbourhood (the subgraph corresponding to all network nodes within \(k\) hops of itself, for some fixed \(k\)), (2) the node from which the message originated, and (3) the incoming port (which of its neighbours last forwarded the message). Our objective is to determine, as \(k\) varies, which of these parameters are necessary and/or sufficient to permit local routing on a network modelled by a connected undirected graph. In particular, we establish tight bounds on \(k\) for the feasibility of deterministic \(k\)-local routing for various combinations of these parameters, as well as corresponding bounds on dilation (the worst-case ratio of actual route length to shortest path length).

## Keywords

Distributed algorithms Local routing Dilation## Notes

### Acknowledgments

The authors wish to thank Therese Biedl who observed that our origin-oblivious and predecessor-oblivious \((n/2)\)-local routing algorithm (Algorithm 3) identifies a shortest path. Also, the authors thank the anonymous reviewers for their helpful suggestions. Some of these results appeared in preliminary form at the 28th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC 2009) [2]. This research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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