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 "explicit convergence rate of a distributed alternating direction method of multipliers"):
  Abstract: Consider a set of N agents seeking to solve distributively the minimization problem $\inf_{x} \sum_{n = 1}^N f_n(x)$ where the convex functions $f_n$ are local to the agents. The popular Alternating Direction Method of Multipliers has the potential to handle distributed optimization problems of this kind. We provide a general reformulation of the problem and obtain a class of distributed algorithms which encompass various network architectures. The rate of convergence of our method is considered. It is assumed that the infimum of the problem is reached at a point $x_\star$, the functions $f_n$ are twice differentiable at this point and $\sum \nabla^2 f_n(x_\star) > 0$ in the positive definite ordering of symmetric matrices. With these assumptions, it is shown that the convergence to the consensus $x_\star$ is linear and the exact rate is provided. Application examples where this rate can be optimized with respect to the ADMM free parameter $\rho$ are also given.

Includes members:
  Member "linear convergence rate of a class of distributed augmented lagrangian algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "cluster based distributed augmented lagrangian algorithm for a class of constrained convex optimization problems")
  Member "asynchronous distributed optimization using a randomized alternating direction method of multipliers":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "popsgd decentralized stochastic gradient descent in the population model")
  Member "a reliable effective terascale linear learning system":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "stannis low power acceleration of deep neural network training using computational storage")
  Member "distributed and recursive parameter estimation in parametrized linear state space models":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "convergence rate analysis of distributed gossip linear parameter estimation fundamental limits and tradeoffs")

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.DC(Distributed, Parallel, and Cluster Computing)