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 general framework for graph sparsification"):
  Abstract: Given a weighted graph $G$ and an error parameter $\epsilon > 0$, the {\em graph sparsification} problem requires sampling edges in $G$ and giving the sampled edges appropriate weights to obtain a sparse graph $G_{\epsilon}$ (containing O(n\log n) edges in expectation) with the following property: the weight of every cut in $G_{\epsilon}$ is within a factor of $(1\pm \epsilon)$ of the weight of the corresponding cut in $G$. We provide a generic framework that sets out sufficient conditions for any particular sampling scheme to result in good sparsifiers, and obtain a set of results by simple instantiations of this framework. The results we obtain include the following: (1) We improve the time complexity of graph sparsification from O(m\log^3 n) to O(m + n\log^4 n) for graphs with polynomial edge weights. (2) We improve the time complexity of graph sparsification from O(m\log^3 n) to O(m\log^2 n) for graphs with arbitrary edge weights. (3) If the size of the sparsifier is allowed to be O(n\log^2 n/\epsilon^2) instead of O(n\log n/\epsilon^2), we improve the time complexity of sparsification to O(m) for graphs with polynomial edge weights. (4) We show that sampling using standard connectivities results in good sparsifiers, thus resolving an open question of Benczur and Karger. As a corollary, we give a simple proof of (a slightly weaker version of) a result due to Spielman and Srivastava showing that sampling using effective resistances produces good sparsifiers. (5) We give a simple proof showing that sampling using strong connectivities results in good sparsifiers, a result obtained previously using a more involved proof by Benczur and Karger. A key ingredient of our proofs is a generalization of bounds on the number of small cuts in an undirected graph due to Karger; this generalization might be of independent interest.

Includes members:
  Member "nearly linear time algorithms for preconditioning and solving symmetric diagonally dominant linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "speeding up linear programming using randomized linear algebra")
  Member "nearly linear time algorithms for graph partitioning graph sparsification and solving linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "compressive sensing for cut improvement and local clustering")

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)