Brief Announcement: Distributed Construction of Near-Optimal Compact Routing Schemes for Planar Graphs

We consider the problem of computing a compact routing scheme for a weighted undirected planar graph G := (V,E,w) in several models. For a given parameter is an element of > 0, we compute a routing scheme with stretch 1 + is an element of and labels and routing tables of size (O) over tilde (is an element of -1). In CONGEST, the construction takes (O) over tilde(is an element of-3 center dot HD) time, where HD denotes the network's hop-diameter. Further, it takes (O) over tilde(is an element of-3) time in a PRAM with O(n) processors and the novel HYBRID model. Thus, our algorithms are almost optimal in all relevant parameters. To achieve these results, we extend the divide-and-conquer framework of Li and Parter [STOC '19] and combine it with state-of-the-art distributed distance approximation algorithms [STOC '22].