APSP
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A Near-Optimal Offline Algorithm for Dynamic All-Pairs Shortest Paths in Planar Digraphs
arXiv:2606.01809v1 Announce Type: new Abstract: In the planar, dynamic All-Pairs Shortest Paths (APSP) problem, a planar, weighted digraph $G$ undergoes a sequence of edge weight updates and the goal is to maintain a data structure on $G$, that can quickly answer distance queries between any two vertices $x,y \in V(G)$. The currently best algorithms for this problem require $\tilde{O}(n^{2/3})$ worst-case update and query time, while conditional lower bounds show that either update or query...
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Announce Type: new Abstract: In this paper, we provide the first deterministic algorithms with sublogarithmic round complexity for spanners and approximate shortest paths in various MPC models. Moreover, we significantly improve upon the state of the art in the deterministic Congested Clique. In particular, we obtain the following four results on undirected graphs: 1.