@inproceedings{18308,
  abstract     = {We study in this paper the problem of maintaining a solution to k-median and k-means clustering in a fully dynamic setting. To do so, we present an algorithm to efficiently maintain a coreset, a compressed version of the dataset, that allows easy computation of a clustering solution at query time. Our coreset algorithm has near-optimal update time of Õ(k) in general metric spaces, which reduces to Õ(d) in the Euclidean space ℝ^d. The query time is O(k²) in general metrics, and O(kd) in ℝ^d. To maintain a constant-factor approximation for k-median and k-means clustering in Euclidean space, this directly leads to an algorithm with update time Õ(d), and query time Õ(kd + k²). To maintain a O(polylog k)-approximation, the query time is reduced to Õ(kd).},
  author       = {La Tour, Max Dupré and Henzinger, Monika H and Saulpic, David},
  booktitle    = {32nd Annual European Symposium on Algorithms},
  isbn         = {9783959773386},
  issn         = {1868-8969},
  location     = {London, United Kingdom},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Fully dynamic k-means coreset in near-optimal update time}},
  doi          = {10.4230/LIPIcs.ESA.2024.100},
  volume       = {308},
  year         = {2024},
}

@inproceedings{18309,
  abstract     = {The problem of designing connectivity oracles supporting vertex failures is one of the basic data structures problems for undirected graphs. It is already well understood: previous works [Duan-Pettie STOC'10; Long-Saranurak FOCS'22] achieve query time linear in the number of failed vertices, and it is conditionally optimal as long as we require preprocessing time polynomial in the size of the graph and update time polynomial in the number of failed vertices. We revisit this problem in the paradigm of algorithms with predictions: we ask if the query time can be improved if the set of failed vertices can be predicted beforehand up to a small number of errors. More specifically, we design a data structure that, given a graph G = (V,E) and a set of vertices predicted to fail D̂ ⊆ V of size d = |D̂|, preprocesses it in time Õ(d|E|) and then can receive an update given as the symmetric difference between the predicted and the actual set of failed vertices D̂△D = (D̂ ⧵ D) ∪ (D ⧵ D̂) of size η = |D̂△D|, process it in time Õ(η⁴), and after that answer connectivity queries in G ⧵ D in time O(η). Viewed from another perspective, our data structure provides an improvement over the state of the art for the fully dynamic subgraph connectivity problem in the sensitivity setting [Henzinger-Neumann ESA'16]. We argue that the preprocessing time and query time of our data structure are conditionally optimal under standard fine-grained complexity assumptions.},
  author       = {Hu, Bingbing and Kosinas, Evangelos and Polak, Adam},
  booktitle    = {32nd Annual European Symposium on Algorithms},
  isbn         = {9783959773386},
  issn         = {1868-8969},
  location     = {London, United Kingdom},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Connectivity oracles for predictable vertex failures}},
  doi          = {10.4230/LIPIcs.ESA.2024.72},
  volume       = {308},
  year         = {2024},
}