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 "preserving distances in very faulty graphs"):
  Abstract: Preservers and additive spanners are sparse (hence cheap to store) subgraphs that preserve the distances between given pairs of nodes exactly or with some small additive error, respectively. Since real-world networks are prone to failures, it makes sense to study fault-tolerant versions of the above structures. This turns out to be a surprisingly difficult task. For every small but arbitrary set of edge or vertex failures, the preservers and spanners need to contain {\em replacement paths} around the faulted set. In this paper we make substantial progress on fault tolerant preservers and additive spanners: #R##N#(1) We present the first truly sub-quadratic size single-pair preservers in unweighted (possibly directed) graphs for \emph{any} fixed number $f$ of faults. Our result indeed generalizes to the single-source case, and can be used to build new fault-tolerant additive spanners (for all pairs). #R##N#(2) The size of the above single-pair preservers is $O(n^{2-g(f)})$ for some positive function $g$, and grows to $O(n^2)$ for increasing $f$. We show that this is necessary even in undirected unweighted graphs, and even if you allow for a small additive error: If you aim at size $O(n^{2-\epsilon})$ for $\epsilon>0$, then the additive error has to be $\Omega(\eps f)$. This surprisingly matches known upper bounds in the literature. #R##N#(3) For weighted graphs, we provide matching upper and lower bounds for the single pair case. Namely, the size of the preserver is $\Theta(n^2)$ for $f\geq 2$ in both directed and undirected graphs, while for $f=1$ the size is $\Theta(n)$ in undirected graphs. For directed graphs, we have a superlinear upper bound and a matching lower bound. #R##N#Most of our lower bounds extend to the distance oracle setting, where rather than a subgraph we ask for any compact data structure.

Includes members:
  Member "connectivity oracles for graphs subject to vertex failures":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "approximate distance oracles subject to multiple vertex failures")
  Member "a hierarchy of lower bounds for sublinear additive spanners":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "exponentially faster shortest paths in the congested clique")
  Member "linear size distance preservers":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "weighted additive spanners")
  Member "dual failure resilient bfs structure":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "approximate distance oracles subject to multiple vertex failures")
  Member "better distance preservers and additive spanners":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")
  Member "the 4 3 additive spanner exponent is tight":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "weighted additive spanners")
  Member "improved purely additive fault tolerant spanners":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "graph spanners a tutorial review")
  Member "fault tolerant approximate shortest path trees":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "approximate distance oracles subject to multiple vertex failures")

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)