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 "vertex sparsifiers and abstract rounding algorithms"):
  Abstract: The notion of vertex sparsification is introduced in \cite{M}, where it was shown that for any graph $G = (V, E)$ and a subset of $k$ terminals $K \subset V$, there is a polynomial time algorithm to construct a graph $H = (K, E_H)$ on just the terminal set so that simultaneously for all cuts $(A, K-A)$, the value of the minimum cut in $G$ separating $A$ from $K -A$ is approximately the same as the value of the corresponding cut in $H$. #R##N#We give the first super-constant lower bounds for how well a cut-sparsifier $H$ can simultaneously approximate all minimum cuts in $G$. We prove a lower bound of $\Omega(\log^{1/4} k)$ -- this is polynomially-related to the known upper bound of $O(\log k/\log \log k)$. This is an exponential improvement on the $\Omega(\log \log k)$ bound given in \cite{LM} which in fact was for a stronger vertex sparsification guarantee, and did not apply to cut sparsifiers. #R##N#Despite this negative result, we show that for many natural problems, we do not need to incur a multiplicative penalty for our reduction. We obtain optimal $O(\log k)$-competitive Steiner oblivious routing schemes, which generalize the results in \cite{R}. We also demonstrate that for a wide range of graph packing problems (which includes maximum concurrent flow, maximum multiflow and multicast routing, among others, as a special case), the integrality gap of the linear program is always at most $O(\log k)$ times the integrality gap restricted to trees. This result helps to explain the ubiquity of the $O(\log k)$ guarantees for such problems. #R##N#Lastly, we use our ideas to give an efficient construction for vertex-sparsifiers that match the current best existential results -- this was previously open. Our algorithm makes novel use of Earth-mover constraints.

Includes members:
  Member "vertex sparsifiers new results from old techniques":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "scattering and sparse partitions and their applications")
  Member "metric extension operators vertex sparsifiers and lipschitz extendability":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "scattering and sparse partitions and their applications")
  Member "sequential and parallel algorithms for mixed packing and covering":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "distributed assignment with limited communication for multi robot multi target tracking")

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)