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 "approximation algorithms for clustering via weighted impurity measures"):
  Abstract: An impurity measures $I:{R}^k \to {R}^+$ maps a $k$-dimensional vector ${\bf v}$ to a non-negative value $I({\bf v})$ so that the more homogeneous ${\bf v}$, the larger its impurity. We study clustering based on impurity measures: given a collection $V$ of $n$ many $k$-dimensional vectors and an impurity measure $I$, the goal is to find a partition ${\cal P}$ of $V$ into $L$ groups $V_1,\ldots,V_L$ that minimizes the total impurities of the groups in ${\cal P}$, i.e., $I({\cal P})= \sum_{m=1}^{L} I(\sum_{{\bf v} \in V_m}{\bf v}).$ #R##N#Impurity minimization is widely used as quality assessment measure in probability distribution clustering and in categorical clustering where it is not possible to rely on geometric properties of the data set. 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. #R##N#Our research contributes to fill this gap. We first present a simple linear time algorithm that simultaneously achieves $3$-approximation for the Gini impurity measure and $O(\log(\sum_{{\bf v} \in V} \| {\bf v} \|_1))$-approximation for the Entropy impurity measure. Then, for the Entropy impurity measure---where we also show that finding the optimal clustering is strongly NP-hard---we are able to design a polynomial time $O(\log^2(\min\{k,L\}))$-approximation algorithm. Our algorithm relies on a nontrivial characterization of a class of clusterings that necessarily includes a partition achieving $O(\log^2(\min\{k,L\}))$--approximation of the impurity of the optimal partition. Remarkably, this is the first polynomial time algorithm with approximation guarantee independent of the number of points/vector and not relying on any restriction on the components of the vectors for producing clusterings with minimum entropy.

Includes members:
  Member "information distilling quantizers":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "information theoretical clustering is hard to approximate")
  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 "information theoretical clustering is hard to approximate")

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)