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 deterministic linear program solver in current matrix multiplication time"):
  Abstract: Interior point algorithms for solving linear programs have been studied extensively for a long time [e.g. Karmarkar 1984; Lee, Sidford FOCS'14; Cohen, Lee, Song STOC'19]. For linear programs of the form $\min_{Ax=b, x \ge 0} c^\top x$ with $n$ variables and $d$ constraints, the generic case $d = \Omega(n)$ has recently been settled by Cohen, Lee and Song [STOC'19]. Their algorithm can solve linear programs in $\tilde O(n^\omega \log(n/\delta))$ expected time, where $\delta$ is the relative accuracy. This is essentially optimal as all known linear system solvers require up to $O(n^{\omega})$ time for solving $Ax = b$. However, for the case of deterministic solvers, the best upper bound is Vaidya's 30 years old $O(n^{2.5} \log(n/\delta))$ bound [FOCS'89]. In this paper we show that one can also settle the deterministic setting by derandomizing Cohen et al.'s $\tilde{O}(n^\omega \log(n/\delta))$ time algorithm. This allows for a strict $\tilde{O}(n^\omega \log(n/\delta))$ time bound, instead of an expected one, and a simplified analysis, reducing the length of their proof of their central path method by roughly half. Derandomizing this algorithm was also an open question asked in Song's PhD Thesis. #R##N#The main tool to achieve our result is a new data-structure that can maintain the solution to a linear system in subquadratic time. More accurately we are able to maintain $\sqrt{U}A^\top(AUA^\top)^{-1}A\sqrt{U}\:v$ in subquadratic time under $\ell_2$ multiplicative changes to the diagonal matrix $U$ and the vector $v$. This type of change is common for interior point algorithms. Previous algorithms [e.g. Vaidya STOC'89; Lee, Sidford FOCS'15; Cohen, Lee, Song STOC'19] required $\Omega(n^2)$ time for this task. [...]

Includes members:
  Member "solving empirical risk minimization in the current matrix multiplication time":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "solving tall dense linear programs in nearly linear time")
  Member "dynamic matrix inverse improved algorithms and matching conditional lower bounds":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "solving tall dense linear programs in nearly linear time")
  Member "distributed edge connectivity in sublinear time":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a deterministic algorithm for balanced cut with applications to dynamic connectivity flows and beyond")
  Member "limits on all known and some unknown approaches to matrix multiplication":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")
  Member "solving linear programs in the current matrix multiplication time":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "solving tall dense linear programs in nearly linear time")
  Member "derandomization beyond connectivity undirected laplacian systems in nearly logarithmic space":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "spectral sparsification via bounded independence sampling")
  Member "improved rectangular matrix multiplication using powers of the coppersmith winograd tensor":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")
  Member "powers of tensors and fast matrix multiplication":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")

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)