human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "optimal vertex fault tolerant spanners for fixed stretch"
  Abstract: A $k$-spanner of a graph $G$ is a sparse subgraph $H$ whose shortest path distances match those of $G$ up to a multiplicative error $k$. In this paper we study spanners that are resistant to faults. A subgraph $H \subseteq G$ is an $f$ vertex fault tolerant (VFT) $k$-spanner if $H \setminus F$ is a $k$-spanner of $G \setminus F$ for any small set $F$ of $f$ vertices that might "fail." One of the main questions in the area is: what is the minimum size of an $f$ fault tolerant $k$-spanner that holds for all $n$ node graphs (as a function of $f$, $k$ and $n$)? This question was first studied in the context of geometric graphs [Levcopoulos et al. STOC '98, Czumaj and Zhao SoCG '03] and has more recently been considered in general undirected graphs [Chechik et al. STOC '09, Dinitz and Krauthgamer PODC '11]. #R##N#In this paper, we settle the question of the optimal size of a VFT spanner, in the setting where the stretch factor $k$ is fixed. Specifically, we prove that every (undirected, possibly weighted) $n$-node graph $G$ has a $(2k-1)$-spanner resilient to $f$ vertex faults with $O_k(f^{1 - 1/k} n^{1 + 1/k})$ edges, and this is fully optimal (unless the famous Erdos Girth Conjecture is false). Our lower bound even generalizes to imply that no data structure capable of approximating $dist_{G \setminus F}(s, t)$ similarly can beat the space usage of our spanner in the worst case. We also consider the edge fault tolerant (EFT) model, defined analogously with edge failures rather than vertex failures. We show that the same spanner upper bound applies in this setting. Our data structure lower bound extends to the case $k=2$ (and hence we close the EFT problem for $3$-approximations), but it falls to $\Omega(f^{1/2 - 1/(2k)} \cdot n^{1 + 1/k})$ for $k \ge 3$. We leave it as an open problem to close this gap.

Connected through hyperedge HE-1 (induced by source paper "approximate distance oracles subject to multiple vertex failures"):
  with members:
    - "sensitive distance and reachability oracles for large batch updates"
    - "generic single edge fault tolerant exact distance oracle"
    - "a trivial yet optimal solution to vertex fault tolerant spanners"
    - "exact distance oracles for planar graphs with failing vertices"
    - "preserving distances in very faulty graphs"
    - "connectivity oracles for graphs subject to vertex failures"
    - "multiple edge fault tolerant approximate shortest path trees"
    - "fully dynamic all pairs shortest paths with worst case update time revisited"

Connected through hyperedge HE-2 (induced by source paper "efficient and simple algorithms for fault tolerant spanners"):
  with members:
    - "a trivial yet optimal solution to vertex fault tolerant spanners"
    - "parallel graph decompositions using random shifts"
    - "improved parallel algorithms for spanners and hopsets"
    - "fault tolerant spanners better and simpler"
    - "transitive closure spanners"
    - "graph sparsification by effective resistances"
    - "randomized approximation schemes for cuts and flows in capacitated graphs"

Connected through hyperedge HE-3 (induced by source paper "a polynomial time algorithm for almost optimal vertex fault tolerant spanners"):
  with members:
    - "a trivial yet optimal solution to vertex fault tolerant spanners"
    - "the greedy spanner is existentially optimal"
    - "fault tolerant spanners better and simpler"

Connected through hyperedge HE-4 (induced by source paper "graph spanners a tutorial review"):
  with members:
    - "near additive spanners and near exact hopsets a unified view"
    - "some general structure for extremal sparsification problems"
    - "weighted additive spanners"
    - "near additive spanners in low polynomial deterministic congest time"
    - "multi level graph sketches via single level solvers"
    - "almost shortest paths and pram distance oracles in weighted graphs"
    - "an fpt algorithm for minimum additive spanner problem"
    - "distributed construction of light networks"

Connected through hyperedge HE-5 (induced by source paper "a trivial yet optimal solution to vertex fault tolerant spanners"):
  with members:
    - "preserving distances in very faulty graphs"
    - "the greedy spanner is existentially optimal"
    - "a hierarchy of lower bounds for sublinear additive spanners"
    - "compact and fast sensitivity oracles for single source distances"
    - "dual failure resilient bfs structure"
    - "the 4 3 additive spanner exponent is tight"
    - "fault tolerant approximate bfs structures"
    - "sparse fault tolerant bfs trees"

Question: Please tell me which class the center node 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)