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 "faster polytope rounding sampling and volume computation via a sublinear ball walk"):
  Abstract: We study the problem of "isotropically rounding" a polytope $K\subset\mathbb{R}^n$, that is, computing a linear transformation which makes the uniform distribution on the polytope have roughly identity covariance matrix. We assume $K$ is defined by $m$ linear inequalities, with guarantee that $rB\subset K\subset RB$, where $B$ is the unit ball. We introduce a new variant of the ball walk Markov chain and show that, roughly, the expected number of arithmetic operations per-step of this Markov chain is $O(m)$ that is sublinear in the input size $mn$--the per-step time of all prior Markov chains. Subsequently, we give a rounding algorithm that succeeds with probability $1-\varepsilon$ in $\tilde{O}(mn^{4.5}\mbox{polylog}(\frac{1}{\varepsilon},\frac{R}{r}))$ arithmetic operations. This gives a factor of $\sqrt{n}$ improvement on the previous bound of $\tilde{O}(mn^5\mbox{polylog}(\frac{1}{\varepsilon},\frac{R}{r}))$ for rounding, which uses the hit-and-run algorithm. Since the rounding preprocessing step is in many cases the bottleneck in improving sampling or volume computation, our results imply these tasks can also be achieved in roughly $\tilde{O}(mn^{4.5}\mbox{polylog}(\frac{1}{\varepsilon},\frac{R}{r})+mn^4\delta^{-2})$ operations for computing the volume of $K$ up to a factor $1+\delta$ and $\tilde{O}(mn^{4.5}\mbox{polylog}(\frac{1}{\varepsilon},\frac{R}{r})))$ for uniformly sampling on $K$ with TV error $\varepsilon$. This improves on the previous bounds of $\tilde{O}(mn^5\mbox{polylog}(\frac{1}{\varepsilon},\frac{R}{r})+mn^4\delta^{-2})$ for volume computation when roughly $m\geq n^{2.5}$, and $\tilde{O}(mn^5\mbox{polylog}(\frac{1}{\varepsilon},\frac{R}{r}))$ for sampling when roughly $m\geq n^{1.5}$. We achieve this improvement by a novel method of computing polytope membership, where one avoids checking inequalities estimated to have a very low probability of being violated.

Includes members:
  Member "convergence rate of riemannian hamiltonian monte carlo and faster polytope volume computation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "strong self concordance and sampling")
  Member "geodesic walks in polytopes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on the approximability of weighted model integration on dnf structures")

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)