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 "refined vertex sparsifiers of planar graphs"):
  Abstract: We study the following version of cut sparsification. Given a large edge-weighted network $G$ with $k$ terminal vertices, compress it into a smaller network $H$ with the same terminals, such that every minimum terminal cut in $H$ approximates the corresponding one in $G$, up to a factor $q\geq 1$ that is called the quality. (The case $q=1$ is known also as a mimicking network). We provide new insights about the structure of minimum terminal cuts, leading to new results for cut sparsifiers of planar graphs. Our first contribution identifies a subset of the minimum terminal cuts, which we call elementary, that generates all the others. Consequently, $H$ is a cut sparsifier if and only if it preserves all the elementary terminal cuts (up to this factor $q$). This structural characterization lead to improved bounds on the size of $H$. For example, it improve the bound of mimicking-network size for planar graphs into a near-optimal one. Our second and main contribution is to refine the known bounds in terms of $\gamma=\gamma(G)$, which is defined as the minimum number of faces that are incident to all the terminals in a planar graph $G$. We prove that the number of elementary terminal cuts is $O((2k/\gamma)^{2\gamma})$ (compared to $O(2^k)$ terminal cuts), and furthermore obtain a mimicking-network of size $O(\gamma 2^{2\gamma} k^4)$, which is near-optimal as a function of $\gamma$. In the analysis we break the elementary terminal cuts into fragments, and count them carefully. Our third contribution is a duality between cut sparsification and distance sparsification for certain planar graphs, when the sparsifier $H$ is required to be a minor of $G$. This duality connects problems that were previously studied separately, implying new results, new proofs of known results, and equivalences between open gaps.

Includes members:
  Member "relaxed voronoi a simple framework for terminal clustering problems":
    also connected through other hyperedges:
      (none)
  Member "steiner point removal with distortion o log k":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "scattering and sparse partitions and their applications")
  Member "improved guarantees for vertex sparsification in planar graphs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "scattering and sparse partitions and their applications")
  Member "an exponential lower bound for cut sparsifiers in planar graphs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a face cover perspective to ell_1 embeddings of planar graphs")
  Member "steiner point removal distant terminals don t really bother":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "scattering and sparse partitions and their applications")
  Member "graph minors for preserving terminal distances approximately lower and upper bounds":
    also connected through other hyperedges:
      - Hyperedge HE-5 (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-6 (induced by source paper "scattering and sparse partitions and their applications")
  Member "on vertex sparsifiers with steiner nodes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (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)