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 "on euclidean k means clustering with alpha center proximity"):
  Abstract: $k$-means clustering is NP-hard in the worst case but previous work has shown efficient algorithms assuming the optimal $k$-means clusters are \emph{stable} under additive or multiplicative perturbation of data. This has two caveats. First, we do not know how to efficiently verify this property of optimal solutions that are NP-hard to compute in the first place. Second, the stability assumptions required for polynomial time $k$-means algorithms are often unreasonable when compared to the ground-truth clusters in real-world data. A consequence of multiplicative perturbation resilience is \emph{center proximity}, that is, every point is closer to the center of its own cluster than the center of any other cluster, by some multiplicative factor $\alpha > 1$. #R##N#We study the problem of minimizing the Euclidean $k$-means objective only over clusterings that satisfy $\alpha$-center proximity. We give a simple algorithm to find the optimal $\alpha$-center-proximal $k$-means clustering in running time exponential in $k$ and $1/(\alpha - 1)$ but linear in the number of points and the dimension. We define an analogous $\alpha$-center proximity condition for outliers, and give similar algorithmic guarantees for $k$-means with outliers and $\alpha$-center proximity. On the hardness side we show that for any $\alpha' > 1$, there exists an $\alpha \leq \alpha'$, $(\alpha >1)$, and an $\varepsilon_0 > 0$ such that minimizing the $k$-means objective over clusterings that satisfy $\alpha$-center proximity is NP-hard to approximate within a multiplicative $(1+\varepsilon_0)$ factor.

Includes members:
  Member "exact algorithms and lower bounds for stable instances of euclidean k means":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "graph pricing with limited supply")
  Member "approximation schemes for clustering with outliers":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "layered sampling for robust optimization problems")
  Member "clustering stable instances of euclidean k means":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "exact algorithms and lower bounds for stable instances of euclidean k means")
  Member "better guarantees for k means and euclidean k median by primal dual algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-4 (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-5 (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-6 (induced by source paper "k means few more steps yield constant approximation")
  Member "k center clustering under perturbation resilience":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "semi bandit optimization in the dispersed setting")
  Member "computational feasibility of clustering under clusterability assumptions":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "on the unreasonable effectiveness of the greedy algorithm greedy adapts to sharpness")

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)