human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "the hardness of approximation of euclidean k means"
  Abstract: The Euclidean $k$-means problem is a classical problem that has been extensively studied in the theoretical computer science, machine learning and the computational geometry communities. In this problem, we are given a set of $n$ points in Euclidean space $R^d$, and the goal is to choose $k$ centers in $R^d$ so that the sum of squared distances of each point to its nearest center is minimized. The best approximation algorithms for this problem include a polynomial time constant factor approximation for general $k$ and a $(1+\epsilon)$-approximation which runs in time $poly(n) 2^{O(k/\epsilon)}$. At the other extreme, the only known computational complexity result for this problem is NP-hardness [ADHP'09]. The main difficulty in obtaining hardness results stems from the Euclidean nature of the problem, and the fact that any point in $R^d$ can be a potential center. This gap in understanding left open the intriguing possibility that the problem might admit a PTAS for all $k,d$. #R##N#In this paper we provide the first hardness of approximation for the Euclidean $k$-means problem. Concretely, we show that there exists a constant $\epsilon > 0$ such that it is NP-hard to approximate the $k$-means objective to within a factor of $(1+\epsilon)$. We show this via an efficient reduction from the vertex cover problem on triangle-free graphs: given a triangle-free graph, the goal is to choose the fewest number of vertices which are incident on all the edges. Additionally, we give a proof that the current best hardness results for vertex cover can be carried over to triangle-free graphs. To show this we transform $G$, a known hard vertex cover instance, by taking a graph product with a suitably chosen graph $H$, and showing that the size of the (normalized) maximum independent set is almost exactly preserved in the product graph using a spectral analysis, which might be of independent interest.

Connected through hyperedge HE-1 (induced by source paper "explainable k means and k medians clustering"):
  with members:
    - "individual fairness for k clustering"
    - "coresets for clustering with fairness constraints"
    - "same cluster querying for overlapping clusters"
    - "online k means clustering"
    - "fair algorithms for clustering"
    - "unexpected effects of online k means clustering"
    - "sequential no substitution k median clustering"
    - "scalable fair clustering"

Connected through hyperedge HE-2 (induced by source paper "simple and sharp analysis of k means"):
  with members:
    - "noisy greedy and not so greedy k means"
    - "submodular optimization in the mapreduce model"
    - "a constant factor bi criteria approximation guarantee for k means"
    - "the power of randomization distributed submodular maximization on massive datasets"
    - "improved and simplified inapproximability for k means"
    - "a new framework for distributed submodular maximization"
    - "a comparative study of efficient initialization methods for the k means clustering algorithm"
    - "a simple d 2 sampling based ptas for k means and other clustering problems"

Connected through hyperedge HE-3 (induced by source paper "k means few more steps yield constant approximation"):
  with members:
    - "a fast approximation scheme for low dimensional k means"
    - "a constant factor bi criteria approximation guarantee for k means"
    - "better guarantees for k means and euclidean k median by primal dual algorithms"
    - "local search yields a ptas for k means in doubling metrics"
    - "local search yields approximation schemes for k means and k median in euclidean and minor free metrics"
    - "on variants of k means clustering"
    - "improved and simplified inapproximability for k means"
    - "scalable k means"

Connected through hyperedge HE-4 (induced by source paper "analysis of ward s method"):
  with members:
    - "metric perturbation resilience"
    - "approximate hierarchical clustering via sparsest cut and spreading metrics"
    - "better guarantees for k means and euclidean k median by primal dual algorithms"
    - "a cost function for similarity based hierarchical clustering"
    - "improved and simplified inapproximability for k means"
    - "computational feasibility of clustering under clusterability assumptions"
    - "analysis of agglomerative clustering"
    - "robust hierarchical clustering"

Connected through hyperedge HE-5 (induced by source paper "a constant fpt approximation algorithm for hard capacitated k means"):
  with members:
    - "constant factor fpt approximation for capacitated k median"
    - "greedy bi criteria approximations for k medians and k means"
    - "better guarantees for k means and euclidean k median by primal dual algorithms"
    - "local search yields a ptas for k means in doubling metrics"
    - "local search yields approximation schemes for k means and k median in euclidean and minor free metrics"
    - "on variants of k means clustering"
    - "an approximation algorithm for uniform capacitated k median problem with 1 epsilon capacity violation"
    - "improved and simplified inapproximability for k means"

Connected through hyperedge HE-6 (induced by source paper "streaming ptas for constrained k means"):
  with members:
    - "performance of johnson lindenstrauss transform for k means and k medians clustering"
    - "semi supervised algorithms for approximately optimal and accurate clustering"
    - "a unified framework for clustering constrained data without locality property"
    - "better guarantees for k means and euclidean k median by primal dual algorithms"
    - "local search yields a ptas for k means in doubling metrics"
    - "local search yields approximation schemes for k means and k median in euclidean and minor free metrics"
    - "faster algorithms for the constrained k means problem"
    - "sampling in space restricted settings"

Connected through hyperedge HE-7 (induced by source paper "tight fpt approximations for k median and k means"):
  with members:
    - "turning big data into tiny data constant size coresets for k means pca and projective clustering"
    - "from gap eth to fpt inapproximability clique dominating set and more"
    - "improved and simplified inapproximability for k means"
    - "the constant inapproximability of the parameterized dominating set problem"
    - "an improved approximation for k median and positive correlation in budgeted optimization"
    - "the parameterized complexity of k biclique"
    - "approximating k median via pseudo approximation"
    - "a unified framework for approximating and clustering data"

Connected through hyperedge HE-8 (induced by source paper "noisy greedy and not so greedy k means"):
  with members:
    - "a constant factor bi criteria approximation guarantee for k means"
    - "better guarantees for k means and euclidean k median by primal dual algorithms"
    - "local search yields a ptas for k means in doubling metrics"
    - "local search yields approximation schemes for k means and k median in euclidean and minor free metrics"
    - "improved and simplified inapproximability for k means"
    - "a comparative study of efficient initialization methods for the k means clustering algorithm"
    - "a unified framework for approximating and clustering data"

Question: Please tell me which class the center node 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.CC(Computational Complexity)