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 "solving systems of linear equations locally and asynchronously"):
  Abstract: We consider approximating a single component of the solution to a system of linear equations $Ax = b$, where $A$ is an invertible real matrix and $b \in \mathbb{R}^n$. If $A$ is either diagonally dominant or positive definite, we can equivalently solve for $x_i$ in $x = Gx + z$ for some $G$ and $z$ such that spectral radius $\rho(G) < 1$. Existing algorithms either focus on computing the full vector $x$ or use Monte Carlo methods to estimate a component $x_i$ under the condition $\|G\|_{\infty} < 1$. We consider the setting where $n$ is large, yet $G$ is sparse, i.e., each row has at most $d$ nonzero entries. We present synchronous and asynchronous randomized variants of a local algorithm which relies on the Neumann series characterization of the component $x_i$, and allows us to limit the sparsity of the vectors involved in the computation, leading to improved convergence rates. Both variants of our algorithm produce an estimate $\hat{x}_i$ such that $|\hat{x}_i - x_i| \leq \epsilon \|x\|_2$, and we provide convergence guarantees when $\|G\|_2 < 1$. We prove that the synchronous local algorithm uses at most $O(\min(d \epsilon^{\ln(d)/\ln(\|G\|_2)}, dn\ln(\epsilon)/\ln(\|G\|_2)))$ multiplications. The asynchronous local algorithm adaptively samples one coordinate to update among the nonzero coordinates of the current iterate in each time step. We prove with high probability that the error contracts by a time varying factor in each step, guaranteeing that the algorithm converges to the correct solution. With probability at least $1 - \delta$, the asynchronous randomized algorithm uses at most $O(\min(d (\epsilon \sqrt{\delta/5})^{-d/(1-\|G\|_2)}, -dn \ln (\epsilon \sqrt{\delta})/(1-\|G\|_2)))$ multiplications. Thus our algorithms obtain an approximation for $x_i$ in constant time with respect to the size of the matrix when $d = O(1)$ and $1/(1-\|G\|_2) = O(1)$ as a function of $n$.

Includes members:
  Member "a distributed algorithm for solving a linear algebraic equation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "lyapunov criterion for stochastic systems and its applications in distributed computation")
  Member "computing the stationary distribution locally":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "loop estimator for discounted values in markov reward processes")
  Member "a simple combinatorial algorithm for solving sdd systems in nearly linear time":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "circulation control for faster minimum cost flow in unit capacity graphs")
  Member "a nearly mlogn time solver for sdd linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "spectral sparsification via bounded independence sampling")
  Member "nearly linear time algorithms for preconditioning and solving symmetric diagonally dominant linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "speeding up linear programming using randomized linear algebra")

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)