Near-Optimal Decremental Hopsets with Applications

Understand

Given a weighted undirected graph $G=(V,E,w)$, a hopset $H$ of hopbound $\beta$ and stretch $(1+\epsilon)$ is a set of edges such that for any pair of nodes $u, v \in V$, there is a path in $G \cup H$ of at most $\beta$ hops, whose length is within a $(1+\epsilon)$ factor from the distance between $u$ and $v$ in $G$.

• We show the first efficient decremental algorithm for maintaining hopsets with a polylogarithmic hopbound.
• The update time of our algorithm matches the best known static algorithm up to polylogarithmic factors.
• All the previous decremental hopset constructions had a superpolylogarithmic (but subpolynomial) hopbound of $2^{\log^{\Omega(1)} n}$ [Bernstein, FOCS'09; HKN, FOCS'14; Chechik, FOCS'18].