Compact Routing with Name Independence

Abstract

This paper is concerned with compact routing schemes for arbitrary undirected networks in the name-independent model first introduced by Awerbuch, Bar-Noy, Linial, and Peleg. A compact routing scheme that uses local routing tables of size $\~{O}(n^{1/2})$, $O(\log^2 n)$-sized packet headers, and stretch bounded by 5 is obtained, where $n$ is the number of nodes in the network. (We use the notation $\~{O}\left(f(n)\right)$ to represent $O(f(n)\log^c{n})$, where $c$ is an arbitrary nonnegative real number, independent of $n$.) Alternative schemes reduce the packet header size to $O(\log n)$ at the cost of either increasing the stretch to 7 or increasing the table size to $\~{O}(n^{2/3})$. For smaller table-size requirements, the ideas in these schemes are generalized to a scheme that uses $O(\log^2 n)$-sized headers and ${O}(k^2n^{2/k})$-sized tables, and achieves a stretch of $\min\{1 + (k-1)(2^{k/2}-2), 16k^2-8k\}$, improving the best previously known name-independent scheme due to Awerbuch and Peleg.