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This paper presents efficient distributed algorithms for a number of fundamental problems in the area of graph sparsification: We provide the first deterministic distributed algorithm that computes an ultra-sparse spanner in polylog(n) rounds in weighted graphs. Concretely, our algorithm outputs a spanning subgraph with only n+o(n) edges in which the pairwise distances are stretched by a factor of at most O(log n · 2^O(log^* n)). We provide a polylog(n)-round deterministic distributed algorithmarXiv:2204.14086v2 fatcat:pecdmzat2vb4peqfeyotx7daee