Universally-Optimal Distributed Shortest Paths and Transshipment via Graph-Based L1-Oblivious Routing
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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 first sub-linear-round distributed algorithm for transshipment. The key technical contribution leading to these results is the first efficient n^o(1)-competitive linear ℓ_1-oblivious routing operator that does not require the use of ℓ_1-embeddings. Our construction is simple, solely based on low-diameter decompositions, and – in contrast to all known constructions – directly produces an oblivious flow instead of just an approximation of the optimal flow cost. This also has the benefit of simplifying the interaction with Sherman's multiplicative weight framework [SODA'17] in the distributed setting and its subsequent rounding procedures.
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