Improved Approximation for the Directed Spanner Problem

TL;DR

This paper presents a new polynomial-time approximation algorithm for the directed k-spanner problem, achieving a better approximation ratio of O((\,( for all k , improving upon previous results.

Contribution

It introduces an improved approximation algorithm for the directed k-spanner problem with a ratio of O(( , surpassing prior bounds.

Findings

Achieves O(( -approximation for directed k-spanners.

Applies to all k  3, with polynomial runtime.

Improves previous O(n^{2/3})-approximation bounds.

Abstract

We prove that the size of the sparsest directed k-spanner of a graph can be approximated in polynomial time to within a factor of $\tilde{O}(\sqrt{n})$, for all k >= 3. This improves the $\tilde{O}(n^{2/3})$-approximation recently shown by Dinitz and Krauthgamer.