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 "better guarantees for k means and euclidean k median by primal dual algorithms"):
  Abstract: Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for $k$-means with a provable guarantee is a simple local search heuristic yielding an approximation guarantee of $9+\epsilon$, a ratio that is known to be tight with respect to such methods. #R##N#We overcome this barrier by presenting a new primal-dual approach that allows us to (1) exploit the geometric structure of $k$-means and (2) to satisfy the hard constraint that at most $k$ clusters are selected without deteriorating the approximation guarantee. Our main result is a $6.357$-approximation algorithm with respect to the standard LP relaxation. Our techniques are quite general and we also show improved guarantees for the general version of $k$-means where the underlying metric is not required to be Euclidean and for $k$-median in Euclidean metrics.

Includes members:
  Member "the power of local search for clustering":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "an o log 1 5 n log log n approximation algorithm for mean isoperimetry and robust k means")
  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 "improved and simplified inapproximability for k means":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "simple and sharp analysis of k means")
  Member "the hardness of approximation of euclidean k means":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "explainable k means and k medians clustering")
  Member "an improved approximation for k median and positive correlation in budgeted optimization":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "individual fairness for k clustering")
  Member "approximating k median via pseudo approximation":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "fair correlation clustering")
  Member "simpler analyses of local search algorithms for facility location":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "individual fairness for k clustering")
  Member "k means requires exponentially many iterations even in the plane":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "analysis of ward s method")

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)