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 "towards optimal running times for optimal transport"):
  Abstract: In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to \mathbb{R}_{\geq 0}$ where $C(i,j)$ quantifies the penalty of transporting a unit of mass from $i$ to $j$, we show how to compute a coupling $X$ between $r$ and $c$ in time $\widetilde{O}\left(n^2 /\epsilon \right)$ whose expected transportation cost is within an additive $\epsilon$ of optimal, where we have assumed that the largest entry of $C$ is bounded by a constant. This improves upon the previously best known running time for this problem of $\widetilde{O}\left(\min\left\{ n^{9/4}/\epsilon, n^2/\epsilon^2 \right\}\right)$. #R##N#We achieve our results by providing reductions from optimal transport to canonical optimization problems for which recent algorithmic efforts have provided nearly-linear time algorithms. Leveraging nearly linear time algorithms for solving packing linear programs and for solving the matrix balancing problem, we obtain two separate proofs of our stated running time. #R##N#Moreover, we show that further algorithmic improvements to our result would be surprising in the sense that any improvement would yield an $o(n^{2.5})$ algorithm for \textit{maximum cardinality bipartite matching}, for which currently the only known algorithms for achieving such a result are based on fast-matrix multiplication.

Includes members:
  Member "computational optimal transport complexity by accelerated gradient descent is better than by sinkhorn s algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "revisiting fixed support wasserstein barycenter computational hardness and efficient algorithms")
  Member "better and simpler error analysis of the sinkhorn knopp algorithm for matrix scaling":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on efficient optimal transport an analysis of greedy and accelerated mirror descent algorithms")
  Member "approximating optimal transport with linear programs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "revisiting fixed support wasserstein barycenter computational hardness and efficient algorithms")
  Member "near linear time approximation algorithms for optimal transport via sinkhorn iteration":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "geometric dataset distances via optimal transport")
  Member "much faster algorithms for matrix scaling":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "flows in almost linear time via adaptive preconditioning")
  Member "matrix scaling and balancing via box constrained newton s method and interior point methods":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "flows in almost linear time via adaptive preconditioning")
  Member "sparsified cholesky solvers for sdd linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "flows in almost linear time via adaptive preconditioning")
  Member "efficient inverse maintenance and faster algorithms for linear programming":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "solving tall dense linear programs in nearly linear time")

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)