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 "positive semidefinite programming mixed parallel and width independent"):
  Abstract: We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent applications in combinatorial optimization, robust learning, and quantum complexity. The current approximate solvers for positive semidefinite programming can handle only pure packing instances, and technical hurdles prevent their generalization to a wider class of positive instances. For a given multiplicative accuracy of $\epsilon$, our algorithm takes $O(\log^3(nd\rho) \cdot \epsilon^{-3})$ parallelizable iterations, where $n$, $d$ are dimensions of the problem and $\rho$ is a width parameter of the instance, generalizing or improving all previous parallel algorithms in the positive linear and semidefinite programming literature. When specialized to pure packing SDPs, our algorithm's iteration complexity is $O(\log^2 (nd) \cdot \epsilon^{-2})$, a slight improvement and derandomization of the state-of-the-art (Allen-Zhu et. al. '16, Peng et. al. '16, Wang et. al. '15). For a wide variety of structured instances commonly found in applications, the iterations of our algorithm run in nearly-linear time. #R##N#In doing so, we give matrix analytic techniques for overcoming obstacles that have stymied prior approaches to this open problem, as stated in past works (Peng et. al. '16, Mahoney et. al. '16). Crucial to our analysis are a simplification of existing algorithms for mixed positive linear programs, achieved by removing an asymmetry caused by modifying covering constraints, and a suite of matrix inequalities whose proofs are based on analyzing the Schur complements of matrices in a higher dimension. We hope that both our algorithm and techniques open the door to improved solvers for positive semidefinite programming, as well as its applications.

Includes members:
  Member "a rank 1 sketch for matrix multiplicative weights":
    also connected through other hyperedges:
      (none)
  Member "non convex matrix completion against a semi random adversary":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efficient structured matrix recovery and nearly linear time algorithms for solving inverse symmetric m matrices")
  Member "high dimensional robust mean estimation in nearly linear time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "list decodable subspace recovery via sum of squares")
  Member "efficient structured matrix recovery and nearly linear time algorithms for solving inverse symmetric m matrices":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a rank 1 sketch for matrix multiplicative weights")
  Member "an sdp based algorithm for linear sized spectral sparsification":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a spectral approach to network design")
  Member "follow the compressed leader faster online learning of eigenvectors and faster mmwu":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "distributed stochastic algorithms for high rate streaming principal component analysis")
  Member "hardness results for structured linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "space hardness of solving structured linear systems")
  Member "using optimization to obtain a width independent parallel simpler and faster positive sdp solver":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "quantum inspired classical sublinear time algorithm for solving low rank semidefinite programming via sampling approaches")

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)