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 "approximate clustering with same cluster queries"):
  Abstract: Ashtiani et al. proposed a Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to make adaptive queries to a domain expert. The queries are of the kind "do two given points belong to the same optimal cluster?" There are many clustering contexts where such same-cluster queries are feasible. Ashtiani et al. exhibited the power of such queries by showing that any instance of the $k$-means clustering problem, with additional margin assumption, can be solved efficiently if one is allowed $O(k^2 \log{k} + k \log{n})$ same-cluster queries. This is interesting since the $k$-means problem, even with the margin assumption, is $\mathsf{NP}$-hard. #R##N#In this paper, we extend the work of Ashtiani et al. to the approximation setting showing that a few of such same-cluster queries enables one to get a polynomial-time $(1 + \varepsilon)$-approximation algorithm for the $k$-means problem without any margin assumption on the input dataset. Again, this is interesting since the $k$-means problem is $\mathsf{NP}$-hard to approximate within a factor $(1 + c)$ for a fixed constant $0 < c < 1$. The number of same-cluster queries used is $\textrm{poly}(k/\varepsilon)$ which is independent of the size $n$ of the dataset. Our algorithm is based on the $D^2$-sampling technique. We also give a conditional lower bound on the number of same-cluster queries showing that if the Exponential Time Hypothesis (ETH) holds, then any such efficient query algorithm needs to make $\Omega \left(\frac{k}{poly \log k} \right)$ same-cluster queries. Our algorithm can be extended for the case when the oracle is faulty. Another result we show with respect to the $k$-means++ seeding algorithm is that a small modification to the $k$-means++ seeding algorithm within the SSAC framework converts it to a constant factor approximation algorithm instead of the well known $O(\log{k})$-approximation algorithm.

Includes members:
  Member "better guarantees for k means and euclidean k median by primal dual algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "fair correlation clustering")
  Member "local algorithms for interactive clustering":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "diameter based interactive structure discovery")

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)