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 "a face cover perspective to ell_1 embeddings of planar graphs"):
  Abstract: It was conjectured by Gupta et al. [Combinatorica04] that every planar graph can be embedded into $\ell_1$ with constant distortion. However, given an $n$-vertex weighted planar graph, the best upper bound on the distortion is only $O(\sqrt{\log n})$, by Rao [SoCG99]. In this paper we study the case where there is a set $K$ of terminals, and the goal is to embed only the terminals into $\ell_1$ with low distortion. In a seminal paper, Okamura and Seymour [J.Comb.Theory81] showed that if all the terminals lie on a single face, they can be embedded isometrically into $\ell_1$. The more general case, where the set of terminals can be covered by $\gamma$ faces, was studied by Lee and Sidiropoulos [STOC09] and Chekuri et al. [J.Comb.Theory13]. The state of the art is an upper bound of $O(\log \gamma)$ by Krauthgamer, Lee and Rika [SODA19]. Our contribution is a further improvement on the upper bound to $O(\sqrt{\log\gamma})$. Since every planar graph has at most $O(n)$ faces, any further improvement on this result, will be a major breakthrough, directly improving upon Rao's long standing upper bound. Moreover, it is well known that the flow-cut gap equals to the distortion of the best embedding into $\ell_1$. Therefore, our result provides a polynomial time $O(\sqrt{\log \gamma})$-approximation to the sparsest cut problem on planar graphs, for the case where all the demand pairs can be covered by $\gamma$ faces.

Includes members:
  Member "flow cut gaps and face covers in planar graphs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "scattering and sparse partitions and their applications")
  Member "nearly eth tight algorithms for planar steiner tree with terminals on few faces":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "flow cut gaps and face covers in planar graphs")
  Member "an exponential lower bound for cut sparsifiers in planar graphs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "mimicking networks parameterized by connectivity")
  Member "metric embedding via shortest path decompositions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "scattering and sparse partitions and their applications")
  Member "refined vertex sparsifiers of planar graphs":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "scattering and sparse partitions and their applications")
  Member "on notions of distortion and an almost minimum spanning tree with constant average distortion":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "scattering and sparse partitions and their applications")
  Member "vertex sparsifiers new results from old techniques":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "scattering and sparse partitions and their applications")
  Member "cops robbers and threatening skeletons padded decomposition for minor free graphs":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "scattering and sparse partitions and their applications")

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)