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 "local search yields a ptas for k means in doubling metrics"):
  Abstract: The most well known and ubiquitous clustering problem encountered in nearly every branch of science is undoubtedly $k$-means: given a set of data points and a parameter $k$, select $k$ centres and partition the data points into $k$ clusters around these centres so that the sum of squares of distances of the points to their cluster centre is minimized. Typically these data points lie $\mathbb{R}^d$ for some $d\geq 2$. #R##N#$k$-means and the first algorithms for it were introduced in the 1950's. Since then, hundreds of papers have studied this problem and many algorithms have been proposed for it. The most commonly used algorithm is known as Lloyd-Forgy, which is also referred to as "the" $k$-means algorithm, and various extensions of it often work very well in practice. However, they may produce solutions whose cost is arbitrarily large compared to the optimum solution. Kanungo et al. [2004] analyzed a simple local search heuristic to get a polynomial-time algorithm with approximation ratio $9+\epsilon$ for any fixed $\epsilon>0$ for $k$-means in Euclidean space. #R##N#Finding an algorithm with a better approximation guarantee has remained one of the biggest open questions in this area, in particular whether one can get a true PTAS for fixed dimension Euclidean space. We settle this problem by showing that a simple local search algorithm provides a PTAS for $k$-means in $\mathbb{R}^d$ for any fixed $d$. More precisely, for any error parameter $\epsilon>0$, the local search algorithm that considers swaps of up to $\rho=d^{O(d)}\cdot{\epsilon}^{-O(d/\epsilon)}$ centres at a time finds a solution using exactly $k$ centres whose cost is at most a $(1+\epsilon)$-factor greater than the optimum. #R##N#Finally, we provide the first demonstration that local search yields a PTAS for the uncapacitated facility location problem and $k$-median with non-uniform opening costs in doubling 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 "theoretical analysis of the k means algorithm a survey":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "distance geometry and data science")
  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 "on variants of k means clustering":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "k means few more steps yield constant approximation")
  Member "the hardness of approximation of euclidean k means":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "explainable k means and k medians clustering")
  Member "the unreasonable success of local search geometric optimization":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "stability and recovery for independence systems")
  Member "an improved approximation for k median and positive correlation in budgeted optimization":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "individual fairness for k clustering")
  Member "approximating k median via pseudo approximation":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "fair correlation clustering")

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)