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 "simple and fast rounding algorithms for directed and node weighted multiway cut"):
  Abstract: In Directed Multiway Cut(Dir-MC) the input is an edge-weighted directed graph $G=(V,E)$ and a set of $k$ terminal nodes $\{s_1,s_2,\ldots,s_k\} \subseteq V$; the goal is to find a min-weight subset of edges whose removal ensures that there is no path from $s_i$ to $s_j$ for any $i \neq j$. In Node-weighted Multiway Cut(Node-MC) the input is a node-weighted undirected graph $G$ and a set of $k$ terminal nodes $\{s_1,s_2,\ldots,s_k\} \subseteq V$; the goal is to remove a min-weight subset of nodes to disconnect each pair of terminals. Dir-MC admits a $2$-approximation [Naor, Zosin '97] and Node-MC admits a $2(1-\frac{1}{k})$-approximation [Garg, Vazirani, Yannakakis '94], both via rounding of LP relaxations. Previous rounding algorithms for these problems, from nearly twenty years ago, are based on careful rounding of an "optimum" solution to an LP relaxation. This is particularly true for Dir-MC for which the rounding relies on a custom LP formulation instead of the natural distance based LP relaxation [Naor, Zosin '97]. #R##N#In this paper we describe extremely simple and near linear-time rounding algorithms for Dir-MC and Node-MC via a natural distance based LP relaxation. The dual of this relaxation is a special case of the maximum multicommodity flow problem. Our algorithms achieve the same bounds as before but have the significant advantage in that they can work with "any feasible" solution to the relaxation. Consequently, in addition to obtaining "book" proofs of LP rounding for these two basic problems, we also obtain significantly faster approximation algorithms by taking advantage of known algorithms for computing near-optimal solutions for maximum multicommodity flow problems. We also investigate lower bounds for Dir-MC when $k=2$ and in particular prove that the integrality gap of the LP relaxation is $2$ even in directed planar graphs.

Includes members:
  Member "computing the k nearest neighbors for all vertices via dijkstra":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "power weighted shortest paths for unsupervised learning")
  Member "local distribution and the symmetry gap approximability of multiway partitioning problems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "optimizing item and subgroup configurations for social aware vr shopping")
  Member "multiway cut pairwise realizable distributions and descending thresholds":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "optimizing item and subgroup configurations for social aware vr shopping")
  Member "multicommodity flows and cuts in polymatroidal networks":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "online energy harvesting problem over an arbitrary directed acyclic graph network")
  Member "approximation algorithms for submodular multiway partition":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "improved approximation algorithms for inventory problems")
  Member "submodular cost allocation problem and applications":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "improved approximation algorithms for inventory problems")
  Member "faster approximation schemes for fractional multicommodity flow problems via dynamic graph algorithms":
    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 "rounding algorithms for a geometric embedding of minimum multiway cut":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "hypergraph cuts with general splitting functions")

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)