Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA) 2021
DOI: 10.1137/1.9781611976465.159
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Coresets for Clustering in Excluded-minor Graphs and Beyond

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Cited by 22 publications
(63 citation statements)
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“…In particular, this algorithm is much faster than the quasi-polynomial time approximation scheme of Feldmann et al [14] for k-Median or Facility Location. The runtime of our algorithm also significantly improves over the exponential dependence on k in the approximation schemes of Becker et al [6], Braverman et al [8] for k-Median.…”
Section: Our Resultsmentioning
confidence: 78%
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“…In particular, this algorithm is much faster than the quasi-polynomial time approximation scheme of Feldmann et al [14] for k-Median or Facility Location. The runtime of our algorithm also significantly improves over the exponential dependence on k in the approximation schemes of Becker et al [6], Braverman et al [8] for k-Median.…”
Section: Our Resultsmentioning
confidence: 78%
“…For this class of graphs, the only known approximation algorithms for clustering that compute (1 + ε)-approximations for any ε > 0 either run in quasi-polynomial time, i.e., QPTASs [14], or with runtime f (h, k, ε) • n for some exponential function f , i.e., parameterized approximation schemes [6,8]. Thus an open problem is to identify polynomial-time approximation schemes (PTASs) for clustering in graphs of constant highway dimension.…”
Section: Introductionmentioning
confidence: 99%
“…for a family of graphs excluding a fixed minor, see Corollary 7. This improves on [BJKW20], whose coreset has size O(k 2 /ε 4 ).…”
Section: Our Resultsmentioning
confidence: 99%
“…A construction similar in spirit to the one for treewidth is therefore possible, as presented in Section 6.3. This builds on the work of [BJKW20].…”
Section: Overview Of Our Techniquesmentioning
confidence: 93%
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