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Shortest paths problems are subject to extensive studies in classicdistributed models such as the CONGEST or Congested Clique. These modelsdictate how nodes may communicate in order to determine shortest paths in adistributed input graph. This article focuses on shortest paths problems in theHYBRID model, which combines local communication along edges of the input graphwith global communication between arbitrary pairs of nodes that is restrictedin terms of bandwidth.  Previous work showed that it takes $\tilde \Omega(\!\sqrt{k})$ rounds in the\hybrid model for each node to learn its distance to $k$ dedicated source nodes(aka the $k$-SSP problem), even for crude approximations. This lower bound wasalso matched with algorithmic solutions for $k \geq n^{2/3}$. However, as $k$gets smaller, the gap between the known upper and lower bounds diverges andeven becomes exponential for a single source. In this work we close this gapfor the whole range of $k$ (up to terms that are polylogarithmic in $n$), bygiving algorithmic solutions for $k$-SSP in $\tilde O\big(\!\sqrt k\big)$rounds for any $k$.

Near Tight Shortest Paths in the Hybrid Model