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 "semi supervised algorithms for approximately optimal and accurate clustering"):
  Abstract: We study $k$-means clustering in a semi-supervised setting. Given an oracle that returns whether two given points belong to the same cluster in a fixed optimal clustering, we investigate the following question: how many oracle queries are sufficient to efficiently recover a clustering that, with probability at least $(1 - \delta)$, simultaneously has a cost of at most $(1 + \epsilon)$ times the optimal cost and an accuracy of at least $(1 - \epsilon)$? #R##N#We show how to achieve such a clustering on $n$ points with $O((k^2 \log n) \cdot m(Q, \epsilon^4, \delta/(k\log n)))$ oracle queries, when the $k$ clusters can be learned with an $\epsilon'$ error and a failure probability $\delta'$ using $m(Q, \epsilon',\delta')$ labeled samples, where $Q$ is the set of candidate cluster centers. We show that $m(Q, \epsilon', \delta')$ is small both for $k$-means instances in Euclidean space and for those in finite metric spaces. We further show that, for the Euclidean $k$-means instances, we can avoid the dependency on $n$ in the query complexity at the expense of an increased dependency on $k$: specifically, we give a slightly more involved algorithm that uses $O( k^4/(\epsilon^2 \delta) + (k^{9}/\epsilon^4) \log(1/\delta) + k \cdot m(Q, \epsilon^4/k, \delta))$ oracle queries. #R##N#Finally, we show that the number of queries required for $(1 - \epsilon)$-accuracy in Euclidean $k$-means must linearly depend on the dimension of the underlying Euclidean space, whereas, for finite metric space $k$-means, this number must at least be logarithmic in the number of candidate centers. This shows that our query complexities capture the right dependencies on the respective parameters.

Includes members:
  Member "approximate clustering with same cluster queries":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "robust clustering oracle and local reconstructor of cluster structure of graphs")
  Member "local search yields a ptas for k means in doubling metrics":
    also connected through other hyperedges:
      - Hyperedge HE-2 (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-3 (induced by source paper "k means few more steps yield constant approximation")

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)