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 "information theoretical clustering is hard to approximate"):
  Abstract: An impurity measures $I: \mathbb{R}^d \mapsto \mathbb{R}^+$ is a function that assigns a $d$-dimensional vector ${\bf v}$ to a non-negative value $I({\bf v})$ so that the more homogeneous ${\bf v}$, with respect to the values of its coordinates, the larger its impurity. A well known example of impurity measures is the Entropy impurity. #R##N#We study the problem of clustering based on impurity measures. Let $V$ be a collection of $n$ many $d$-dimensional vectors with non-negative components. Given $V$ and an impurity measure $I$, the goal is to find a partition ${\mathcal P}$ of $V$ into $k$ groups $V_1,\ldots,V_k$ so as to minimize the sum of the impurities of the groups in ${\cal P}$, i.e., $I({\cal P})= \sum_{i=1}^{k} I\bigg(\sum_{ {\bf v} \in V_i} {\bf v} \bigg).$ #R##N#Impurity minimization has been widely used as quality assessment measure in probability distribution clustering (KL-divergence) as well as in categorical clustering. However, in contrast to the case of metric based clustering, the current knowledge of impurity measure based clustering in terms of approximation and inapproximability results is very limited. Here, we contribute to change this scenario by proving that for the Entropy impurity measure the problem does not admit a PTAS even when all vectors have the same $\ell_1$ norm. This result solves a question that remained open in previous work on this topic [Chaudhuri and McGregor COLT 08; Ackermann et. al. ECCC 11].

Includes members:
  Member "approximation algorithms for clustering via weighted impurity measures":
    also connected through other hyperedges:
      (none)
  Member "information distilling quantizers":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "approximation algorithms for clustering via weighted impurity measures")
  Member "greedy merge degrading has optimal power law":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "locality sensitive hashing for f divergences mutual information loss and beyond")
  Member "the hardness of approximation of euclidean k means":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "explainable k means and k medians clustering")
  Member "channel upgradation for non binary input alphabets and macs":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "universal polarization for processes with memory")
  Member "how to construct polar codes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "polar codes and their quantum domain counterparts")
  Member "quantization of binary input discrete memoryless channels":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "intelligence physics and information the tradeoff between accuracy and simplicity in machine learning")
  Member "approximation algorithms for bregman co clustering and tensor clustering":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "approximation algorithms for clustering via weighted impurity measures")

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)