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 norms of graph spanners"):
  Abstract: A $t$-spanner of a graph $G$ is a subgraph $H$ in which all distances are preserved up to a multiplicative $t$ factor. A classical result of Althofer et al. is that for every integer $k$ and every graph $G$, there is a $(2k-1)$-spanner of $G$ with at most $O(n^{1+1/k})$ edges. But for some settings the more interesting notion is not the number of edges, but the degrees of the nodes. This spurred interest in and study of spanners with small maximum degree. However, this is not necessarily a robust enough objective: we would like spanners that not only have small maximum degree, but also have "few" nodes of "large" degree. To interpolate between these two extremes, in this paper we initiate the study of graph spanners with respect to the $\ell_p$-norm of their degree vector, thus simultaneously modeling the number of edges (the $\ell_1$-norm) and the maximum degree (the $\ell_{\infty}$-norm). We give precise upper bounds for all ranges of $p$ and stretch $t$: we prove that the greedy $(2k-1)$-spanner has $\ell_p$ norm of at most $\max(O(n), O(n^{(k+p)/(kp)}))$, and that this bound is tight (assuming the Erdős girth conjecture). We also study universal lower bounds, allowing us to give "generic" guarantees on the approximation ratio of the greedy algorithm which generalize and interpolate between the known approximations for the $\ell_1$ and $\ell_{\infty}$ norm. Finally, we show that at least in some situations, the $\ell_p$ norm behaves fundamentally differently from $\ell_1$ or $\ell_{\infty}$: there are regimes ($p=2$ and stretch $3$ in particular) where the greedy spanner has a provably superior approximation to the generic guarantee.

Includes members:
  Member "sherali adams integrality gaps matching the log density threshold":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "reducibility and computational lower bounds for problems with planted sparse structure")
  Member "the greedy spanner is existentially optimal":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a polynomial time algorithm for almost optimal vertex fault tolerant spanners")
  Member "minimizing the union tight approximations for small set bipartite vertex expansion":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "reducibility and computational lower bounds for problems with planted sparse structure")
  Member "label cover instances with large girth and the hardness of approximating basic k spanner":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "graph spanners a tutorial review")
  Member "fault tolerant spanners better and simpler":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximate distance oracles subject to multiple vertex failures")
  Member "directed spanners via flow based linear programs":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "lasserre integrality gaps for graph spanners and related problems")
  Member "transitive closure spanners":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "efficient and simple algorithms for fault tolerant spanners")

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)