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 "exact algorithms and lower bounds for stable instances of euclidean k means"):
  Abstract: We investigate the complexity of solving stable or perturbation-resilient instances of k-Means and k-Median clustering in fixed dimension Euclidean metrics (or more generally doubling metrics). The notion of stable or perturbation resilient instances was introduced by Bilu and Linial [2010] and Awasthi et al. [2012]. In our context we say a k-Means instance is \alpha-stable if there is a unique OPT solution which remains unchanged if distances are (non-uniformly) stretched by a factor of at most \alpha. Stable clustering instances have been studied to explain why heuristics such as Lloyd's algorithm perform well in practice. In this work we show that for any fixed \epsilon>0, (1+\epsilon)-stable instances of k-Means in doubling metrics can be solved in polynomial time. More precisely we show a natural multiswap local search algorithm in fact finds the OPT solution for (1+\epsilon)-stable instances of k-Means and k-Median in a polynomial number of iterations. We complement this result by showing that under a plausible PCP hypothesis this is essentially tight: that when the dimension d is part of the input, there is a fixed \epsilon_0>0 s.t. there is not even a PTAS for (1+\epsilon_0)-stable k-Means in R^d unless NP=RP. To do this, we consider a robust property of CSPs; call an instance stable if there is a unique optimum solution x^* and for any other solution x', the number of unsatisfied clauses is proportional to the Hamming distance between x^* and x'. Dinur et al. have already shown stable QSAT is hard to approximate for some constant Q, our hypothesis is simply that stable QSAT with bounded variable occurrence is also hard. Given this hypothesis, we consider "stability-preserving" reductions to prove our hardness for stable k-Means. Such reductions seem to be more fragile than standard L-reductions and may be of further use to demonstrate other stable optimization problems are hard.

Includes members:
  Member "clustering stable instances of euclidean k means":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on euclidean k means clustering with alpha center proximity")
  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")
  Member "bilu linial stable instances of max cut and minimum multiway cut":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "solving k 1 stable instances of k terminal cut with isolating cuts")
  Member "on the practically interesting instances of maxcut":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "bilu linial stability certified algorithms and the independent set problem")

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)