Paper detail

Improved Distributed Steiner Forest Construction

We present new distributed algorithms for constructing a Steiner Forest in the CONGEST model. Our deterministic algorithm finds, for any given constant $ε>0$, a $(2+ε)$-approximation in $\tilde{O}(sk+\sqrt{\min(st,n)})$ rounds, where $s$ is the shortest path diameter, $t$ is the number of terminals, $k$ is the number of terminal components in the input, and $n$ is the number of nodes. Our randomized algorithm finds, with high probability, an $O(\log n)$- approximation in time $\tilde{O}(k+\min(s,\sqrt n)+D)$, where $D$ is the unweighted diameter of the network. We also prove a matching lower bound of $\tildeΩ(k+\min(s,\sqrt{n})+D)$ on the running time of any distributed approximation algorithm for the Steiner Forest problem. Previous algorithms were randomized, and obtained either an $O(\log n)$-approximation in $\tilde{O}(sk)$ time, or an $O(1/ε)$-approximation in $\tilde{O}((\sqrt{n}+t)^{1+ε}+D)$ time.