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 directed laplacian systems in nearly linear time through sparse lu factorizations"):
  Abstract: We show how to solve directed Laplacian systems in nearly-linear time. Given a linear system in an $n \times n$ Eulerian directed Laplacian with $m$ nonzero entries, we show how to compute an $\epsilon$-approximate solution in time $O(m \log^{O(1)} (n) \log (1/\epsilon))$. Through reductions from [Cohen et al. FOCS'16] , this gives the first nearly-linear time algorithms for computing $\epsilon$-approximate solutions to row or column diagonally dominant linear systems (including arbitrary directed Laplacians) and computing $\epsilon$-approximations to various properties of random walks on directed graphs, including stationary distributions, personalized PageRank vectors, hitting times, and escape probabilities. These bounds improve upon the recent almost-linear algorithms of [Cohen et al. STOC'17], which gave an algorithm to solve Eulerian Laplacian systems in time $O((m+n2^{O(\sqrt{\log n \log \log n})})\log^{O(1)}(n \epsilon^{-1}))$. #R##N#To achieve our results, we provide a structural result that we believe is of independent interest. We show that Laplacians of all strongly connected directed graphs have sparse approximate LU-factorizations. That is, for every such directed Laplacian $ {\mathbf{L}}$, there is a lower triangular matrix $\boldsymbol{\mathit{\mathfrak{L}}}$ and an upper triangular matrix $\boldsymbol{\mathit{\mathfrak{U}}}$, each with at most $\tilde{O}(n)$ nonzero entries, such that their product $\boldsymbol{\mathit{\mathfrak{L}}} \boldsymbol{\mathit{\mathfrak{U}}}$ spectrally approximates $ {\mathbf{L}}$ in an appropriate norm. This claim can be viewed as an analogue of recent work on sparse Cholesky factorizations of Laplacians of undirected graphs. We show how to construct such factorizations in nearly-linear time and prove that, once constructed, they yield nearly-linear time algorithms for solving directed Laplacian systems.

Includes members:
  Member "sampling random spanning trees faster than matrix multiplication":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "fully dynamic spectral vertex sparsifiers and applications")
  Member "faster algorithms for computing the stationary distribution simulating random walks and more":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "spectral sparsification via bounded independence sampling")
  Member "computing maximum flow with augmenting electrical flows":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "faster divergence maximization for faster maximum flow")
  Member "on fully dynamic graph sparsifiers":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "fully dynamic spectral vertex sparsifiers and applications")
  Member "approximate gaussian elimination for laplacians fast sparse and simple":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a deterministic algorithm for balanced cut with applications to dynamic connectivity flows and beyond")
  Member "almost linear time algorithms for markov chains and new spectral primitives for directed graphs":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "flows in almost linear time via adaptive preconditioning")
  Member "sparsified cholesky and multigrid solvers for connection laplacians":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "a deterministic algorithm for balanced cut with applications to dynamic connectivity flows and beyond")
  Member "sparsified cholesky solvers for sdd linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "flows in almost linear time via adaptive preconditioning")

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)