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Near-Optimal Compression for the Planar Graph Metric
[chapter]

2018
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Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
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The Planar Graph Metric Compression Problem is to compactly encode the distances among k nodes in a planar graph of size n. Two naïve solutions are to store the graph using O(n) bits, or to explicitly store the distance matrix with O(k 2 log n) bits. The only lower bounds are from the seminal work of Gavoille, Peleg, Pérennes, and Raz [SODA'01], who rule out compressions into a polynomially smaller number of bits, for weighted planar graphs, but leave a large gap for unweighted planar graphs.

doi:10.1137/1.9781611975031.35
dblp:conf/soda/AbboudGMW18
fatcat:q25ljpjydvbrnhbd3igman3zq4