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 "expanders via local edge flips"):
  Abstract: Designing distributed and scalable algorithms to improve network connectivity is a central topic in peer-to-peer networks. In this paper we focus on the following well-known problem: given an $n$-node $d$-regular network for $d=\Omega(\log n)$, we want to design a decentralized, local algorithm that transforms the graph into one that has good connectivity properties (low diameter, expansion, etc.) without affecting the sparsity of the graph. To this end, Mahlmann and Schindelhauer introduced the random "flip" transformation, where in each time step, a random pair of vertices that have an edge decide to `swap a neighbor'. They conjectured that performing $O(n d)$ such flips at random would convert any connected $d$-regular graph into a $d$-regular expander graph, with high probability. However, the best known upper bound for the number of steps is roughly $O(n^{17} d^{23})$, obtained via a delicate Markov chain comparison argument. #R##N#Our main result is to prove that a natural instantiation of the random flip produces an expander in at most $O(n^2 d^2 \sqrt{\log n})$ steps, with high probability. Our argument uses a potential-function analysis based on the matrix exponential, together with the recent beautiful results on the higher-order Cheeger inequality of graphs. We also show that our technique can be used to analyze another well-studied random process known as the `random switch', and show that it produces an expander in $O(n d)$ steps with high probability.

Includes members:
  Member "spectral sparsification and regret minimization beyond matrix multiplicative updates":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a spectral approach to network design")
  Member "the switch markov chain for sampling irregular graphs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "moments of uniform random multigraphs with fixed degree sequences")
  Member "tight bounds for rumor spreading with vertex expansion":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the capacity of smartphone peer to peer networks")
  Member "improved cheeger s inequality analysis of spectral partitioning algorithms through higher order spectral gap":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "efficient algorithms for the potts model on small set expanders")
  Member "tight bounds for randomized load balancing on arbitrary network topologies":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "parallel balanced allocations the heavily loaded case")
  Member "simple fast and deterministic gossip and rumor spreading":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "network coding gaps for completion times of multiple unicasts")
  Member "dex self healing expanders":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "some problems in compact message passing")
  Member "twice ramanujan sparsifiers":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "sketching transformed matrices with applications to natural language processing")

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)