algorithms-optimization / Planar graph algorithms
For a designated face of an undirected unweighted planar graph, how many distinct distance patterns can vertices have? Li and Parter (STOC 2019) proved an upper bound; Mozes, Wallheimer and Weimann conjectured the true answer matches their lower bound. Proved, closing the gap.
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Three immediate consequences follow for undirected unweighted planar graphs: better compression of the Okamura-Seymour metric, less space for constant-time exact distance oracles, and a faster distributed algorithm.
Research memory
For a designated face of an undirected unweighted planar graph, how many distinct distance patterns can vertices have? Li and Parter (STOC 2019) proved an upper bound; Mozes, Wallheimer and Weimann conjectured the true answer matches their lower bound. Proved, closing the gap.
Three immediate consequences follow for undirected unweighted planar graphs: better compression of the Okamura-Seymour metric, less space for constant-time exact distance oracles, and a faster distributed algorithm.
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