human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "noisy greedy and not so greedy k means"):
  Abstract: The k-means++ algorithm due to Arthur and Vassilvitskii has become the most popular seeding method for Lloyd's algorithm. It samples the first center uniformly at random from the data set and the other $k-1$ centers iteratively according to $D^2$-sampling where the probability that a data point becomes the next center is proportional to its squared distance to the closest center chosen so far. k-means++ is known to achieve an approximation factor of $O(\log k)$ in expectation. Already in the original paper on k-means++, Arthur and Vassilvitskii suggested a variation called greedy k-means++ algorithm in which in each iteration multiple possible centers are sampled according to $D^2$-sampling and only the one that decreases the objective the most is chosen as a center for that iteration. It is stated as an open question whether this also leads to an $O(\log k)$-approximation (or even better). We show that this is not the case by presenting a family of instances on which greedy k-means++ yields only an $\Omega(\ell\cdot \log k)$-approximation in expectation where $\ell$ is the number of possible centers that are sampled in each iteration. We also study a variation, which we call noisy k-means++ algorithm. In this variation only one center is sampled in every iteration but not exactly by $D^2$-sampling anymore. Instead in each iteration an adversary is allowed to change the probabilities arising from $D^2$-sampling individually for each point by a factor between $1-\epsilon_1$ and $1+\epsilon_2$ for parameters $\epsilon_1 \in [0,1)$ and $\epsilon_2 \ge 0$. We prove that noisy k-means++ compute an $O(\log^2 k)$-approximation in expectation. We also discuss some applications of this result.

Includes members:
  Member "a constant factor bi criteria approximation guarantee for k means":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "simple and sharp analysis of k means")
  Member "better guarantees for k means and euclidean k median by primal dual algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "fair correlation clustering")
  Member "local search yields a ptas for k means in doubling metrics":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "k means few more steps yield constant approximation")
  Member "local search yields approximation schemes for k means and k median in euclidean and minor free metrics":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "k means few more steps yield constant approximation")
  Member "improved and simplified inapproximability for k means":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "simple and sharp analysis of k means")
  Member "the hardness of approximation of euclidean k means":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "explainable k means and k medians clustering")
  Member "a comparative study of efficient initialization methods for the k means clustering algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "a unified framework for approximating and clustering data":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "approximating spectral clustering via sampling a review")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.DS(Data Structures and Algorithms)