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 "analysis of ward s method"):
  Abstract: We study Ward's method for the hierarchical $k$-means problem. This popular greedy heuristic is based on the \emph{complete linkage} paradigm: Starting with all data points as singleton clusters, it successively merges two clusters to form a clustering with one cluster less. The pair of clusters is chosen to (locally) minimize the $k$-means cost of the clustering in the next step. #R##N#Complete linkage algorithms are very popular for hierarchical clustering problems, yet their theoretical properties have been studied relatively little. For the Euclidean $k$-center problem, Ackermann et al. show that the $k$-clustering in the hierarchy computed by complete linkage has a worst-case approximation ratio of $\Theta(\log k)$. If the data lies in $\mathbb{R}^d$ for constant dimension $d$, the guarantee improves to $\mathcal{O}(1)$, but the $\mathcal{O}$-notation hides a linear dependence on $d$. Complete linkage for $k$-median or $k$-means has not been analyzed so far. #R##N#In this paper, we show that Ward's method computes a $2$-approximation with respect to the $k$-means objective function if the optimal $k$-clustering is well separated. If additionally the optimal clustering also satisfies a balance condition, then Ward's method fully recovers the optimum solution. These results hold in arbitrary dimension. We accompany our positive results with a lower bound of $\Omega((3/2)^d)$ for data sets in $\mathbb{R}^d$ that holds if no separation is guaranteed, and with lower bounds when the guaranteed separation is not sufficiently strong. Finally, we show that Ward produces an $\mathcal{O}(1)$-approximative clustering for one-dimensional data sets.

Includes members:
  Member "metric perturbation resilience":
    also connected through other hyperedges:
      (none)
  Member "approximate hierarchical clustering via sparsest cut and spreading metrics":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "hierarchical correlation clustering and tree preserving embedding")
  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 "a cost function for similarity based hierarchical clustering":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "hierarchical correlation clustering and tree preserving embedding")
  Member "improved and simplified inapproximability for k means":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "simple and sharp analysis of k means")
  Member "computational feasibility of clustering under clusterability assumptions":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the unreasonable effectiveness of the greedy algorithm greedy adapts to sharpness")
  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 "analysis of agglomerative clustering":
    also connected through other hyperedges:
      (none)

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)