Exponentially Faster Shortest Paths in the Congested Clique

We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. obtain poly(log log n )-round following problems unweighted undirected -vertex graphs: ( 1 + ϵ )-approximation multi-source (MSSP) from O (√ ) sources. (2 all pairs (APSP). (1 , β)-approximation APSP where β = (log / . These bounds improve exponentially over state-of-the-art poly-logarithmic due to [Censor-Hillel et al., PODC19]. It also provides first nearly-additive problem sub-polynomial time. Our approach is based on distinguishing between short and long distances some distance threshold t Handling done by devising a new algorithm computing sparse emulator with edges. For distances, we provide distance-sensitive variants tool-kit By exploiting fact that this should be applied only local balls radius their round complexities get poly ). Finally, our solutions these are derandomization scheme novel variant hitting set problem, which might independent interest.