Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms 2018
DOI: 10.1137/1.9781611975031.35
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Near-Optimal Compression for the Planar Graph Metric

Abstract: 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, Prennes, 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. For example, when … Show more

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Cited by 14 publications
(38 citation statements)
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References 68 publications
(125 reference statements)
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“…This approach is inspired by the approximate diameter algorithm of Weimann and Yuster [WY16], and the metric compression problem by Abboud at el. [AGMW18]. We start by defining the following problem, a special case of Abboud at el., which will underlie the combinatorial basis for our diameter computation.…”
Section: Our Resultsmentioning
confidence: 99%
See 2 more Smart Citations
“…This approach is inspired by the approximate diameter algorithm of Weimann and Yuster [WY16], and the metric compression problem by Abboud at el. [AGMW18]. We start by defining the following problem, a special case of Abboud at el., which will underlie the combinatorial basis for our diameter computation.…”
Section: Our Resultsmentioning
confidence: 99%
“…This problem can observed as a special case of the metric compression problem studied by Abboud et al [AGMW18]. In particular, [AGMW18] considered an arbitrary subset S ⊆ V with the objective to compress the S × S distances (rather than the S × T distances).…”
Section: The Metric Compression Problemmentioning
confidence: 99%
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“…Our representation of M is as follows, and fairly standard [2,16,35]. We define a (k − 1) × (k − 1) matrix P , satisfying…”
Section: Fr-dijkstramentioning
confidence: 99%

An Almost Optimal Edit Distance Oracle

Charalampopoulos,
Gawrychowski,
Mozes
et al. 2021
Preprint
Self Cite
“…They did not calculate the exact constant, but later experimental comparison by Fischer [16] showed that, even after some tweaking, in the worst case it is around 8. In a later paper, Alstrup et al [9] showed an NCA labeling scheme with labels of length 2.772 log n+O(1) 1 and proved that any such scheme needs labels of length at least 1.008 log n − O (1). The latter non-trivially improves an immediate lower bound of log n + Ω(log log n) obtained from ancestry.…”
Section: Introductionmentioning
confidence: 98%