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 "symmetric and asymmetric k center clustering under stability"):
  Abstract: The k-center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case instances: a 2-approximation for symmetric k-center and an $O(\log^*(k))$-approximation for the asymmetric version. In this work, we go beyond the worst case and provide strong positive results both for the asymmetric and symmetric k-center problems under a very natural input stability (promise) condition called $\alpha$-perturbation resilience \cite{bilu2012stable}, which states that the optimal solution does not change under any $\alpha$-factor perturbation to the input distances. We show that by merely assuming 2-perturbation resilience, the exact solution for the asymmetric k-center problem can be found in polynomial time. To our knowledge, this is the first problem that is hard to approximate to any constant factor in the worst case, yet can be optimally solved in polynomial time under perturbation resilience for a constant value of $\alpha$. Furthermore, we prove our result is tight by showing symmetric k-center under $(2-\epsilon)$-perturbation resilience is hard unless $NP=RP$. This is the first tight result for any problem under perturbation resilience, i.e., the first time the exact value of $\alpha$ for which the problem switches from being NP-hard, to efficiently computable, has been found. #R##N#Our results illustrate a surprising relationship between symmetric and asymmetric k-center instances under perturbation resilience. Unlike approximation ratio, for which symmetric k-center is easily solved to a factor of 2 but asymmetric k-center cannot be approximated to any constant factor, both symmetric and asymmetric k-center can be solved optimally under resilience to 2-perturbations.

Includes members:
  Member "decompositions of triangle dense graphs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "mrattractor detecting communities from large scale graphs")
  Member "beyond worst case analysis in private singular vector computation":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "pd ml lite private distributed machine learning from lighweight cryptography")
  Member "data stability in clustering a closer look":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on euclidean k means clustering with alpha center proximity")
  Member "the complexity of planar counting problems":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "who witnesses the witness finding witnesses in the witness is hard and sometimes impossible")

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)