On Efficient Distributed Construction of Near Optimal Routing Schemes

TL;DR

This paper presents a distributed algorithm for constructing near-optimal routing schemes with nearly matching lower bounds, achieving efficient routing table sizes, low stretch, and optimal running time in distributed networks.

Contribution

It introduces a distributed algorithm that nearly matches the lower bounds for routing scheme construction, improving on previous methods in efficiency and table size.

Findings

Matches the lower bound of rac{rac{n^{1/2}+D}{}} rounds.

Routing tables of size rac{n^{1/k}}{}, labels of size O(k log^2 n).

Stretch factor at most 4k-5+o(1).

Abstract

Given a distributed network represented by a weighted undirected graph $G=(V,E)$ on $n$ vertices, and a parameter $k$, we devise a distributed algorithm that computes a routing scheme in $(n^{1/2+1/k}+D)\cdot n^{o(1)}$ rounds, where $D$ is the hop-diameter of the network. The running time matches the lower bound of $\tilde{\Omega}(n^{1/2}+D)$ rounds (which holds for any scheme with polynomial stretch), up to lower order terms. The routing tables are of size $\tilde{O}(n^{1/k})$, the labels are of size $O(k\log^2n)$, and every packet is routed on a path suffering stretch at most $4k-5+o(1)$. Our construction nearly matches the state-of-the-art for routing schemes built in a centralized sequential manner. The previous best algorithms for building routing tables in a distributed small messages model were by \cite[STOC 2013]{LP13} and \cite[PODC 2015]{LP15}. The former has similar properties but suffers from substantially larger routing tables of size $O(n^{1/2+1/k})$, while the latter has sub-optimal running time of $\tilde{O}(\min\{(nD)^{1/2}\cdot n^{1/k},n^{2/3+2/(3k)}+D\})$.