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We provide universally-optimal distributed graph algorithms for (1+ε)-approximate shortest path problems including shortest-path-tree and transshipment. The universal optimality of our algorithms guarantees that, on any n-node network G, our algorithm completes in T · n^o(1) rounds whenever a T-round algorithm exists for G. This includes D · n^o(1)-round algorithms for any planar or excluded-minor network. Our algorithms never require more than (√(n) + D) · n^o(1) rounds, resulting in the firstarXiv:2110.15944v1 fatcat:tp5f5v5iinfqtmxofqdi64d2lu