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 "the power of recourse better algorithms for facility location in online and dynamic models"):
  Abstract: In this paper we study the facility location problem in the online with recourse and dynamic algorithm models. In the online with recourse model, clients arrive one by one and our algorithm needs to maintain good solutions at all time steps with only a few changes to the previously made decisions (called recourse). We show that the classic local search technique can lead to a $(1+\sqrt{2}+\epsilon)$-competitive online algorithm for facility location with only $O\left(\frac{\log n}{\epsilon}\log\frac1\epsilon\right)$ amortized facility and client recourse. We then turn to the dynamic algorithm model for the problem, where the main goal is to design fast algorithms that maintain good solutions at all time steps. We show that the result for online facility location, combined with the randomized local search technique of Charikar and Guha [10], leads to an $O(1+\sqrt{2}+\epsilon)$ approximation dynamic algorithm with amortized update time of $\tilde O(n)$ in the incremental setting. Notice that the running time is almost optimal, since in general metric space it takes $\Omega(n)$ time to specify a new client's position. The approximation factor of our algorithm also matches the best offline analysis of the classic local search algorithm. Finally, we study the fully dynamic model for facility location, where clients can both arrive and depart. Our main result is an $O(1)$-approximation algorithm in this model with $O(|F|)$ preprocessing time and $O(\log^3 D)$ amortized update time for the HST metric spaces. Using the seminal results of Bartal [4] and Fakcharoenphol, Rao and Talwar [17], which show that any arbitrary $N$-point metric space can be embedded into a distribution over HSTs such that the expected distortion is at most $O(\log N)$, we obtain a $O(\log |F|)$ approximation with preprocessing time of $O(|F|^2\log |F|)$ and $O(\log^3 D)$ amortized update time.

Includes members:
  Member "a tree structure for dynamic facility location":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "constant factor approximation algorithms for parity constrained facility location problems")
  Member "facility location problem in differential privacy model revisited":
    also connected through other hyperedges:
      (none)
  Member "online facility location with deletions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "constant factor approximation algorithms for parity constrained facility location problems")
  Member "online bipartite matching with amortized o log 2 n replacements":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")
  Member "online and dynamic algorithms for set cover":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "an improved algorithm for dynamic set cover")
  Member "efficient construction of probabilistic tree embeddings":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "improved parallel cache oblivious algorithms for dynamic programming and linear algebra")
  Member "facility location in evolving metrics":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "multistage graph problems on a global budget")
  Member "online network design algorithms via hierarchical decompositions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "tight bounds for online weighted tree augmentation")

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)