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 "efficient algorithms for constructing very sparse spanners and emulators"):
  Abstract: Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k = 1,2,\ldots$, constructs an $O(k)$-spanner of an input unweighted $n$-vertex graph with $O(n^{1+1/k})$ expected edges in $O(k)$ rounds of communication. In this paper we improve the result of \cite{MPVX15}, by showing a $k$-round distributed algorithm in the same model, that constructs a $(2k-1)$-spanner with $O(n^{1+1/k}/\epsilon)$ edges, with probability $1- \epsilon$, for any $\epsilon>0$. Moreover, when $k = \omega(\log n)$, our algorithm produces (still in $k$ rounds) {\em ultra-sparse} spanners, i.e., spanners of size $n(1+ o(1))$, with probability $1- o(1)$. To our knowledge, this is the first distributed algorithm in the CONGEST or in the PRAM models that constructs spanners or skeletons (i.e., connected spanning subgraphs) that sparse. Our algorithm can also be implemented in linear time in the standard centralized model, and for large $k$, it provides spanners that are sparser than any other spanner given by a known (near-)linear time algorithm. #R##N#We also devise improved bounds (and algorithms realizing these bounds) for $(1+\epsilon,\beta)$-spanners and emulators. In particular, we show that for any unweighted $n$-vertex graph and any $\epsilon > 0$, there exists a $(1+ \epsilon, ({{\log\log n} \over \epsilon})^{\log\log n})$-emulator with $O(n)$ edges. All previous constructions of $(1+\epsilon,\beta)$-spanners and emulators employ a superlinear number of edges, for all choices of parameters. #R##N#Finally, we provide some applications of our results to approximate shortest paths' computation in unweighted graphs.

Includes members:
  Member "the greedy spanner is existentially optimal":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a polynomial time algorithm for almost optimal vertex fault tolerant spanners")
  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 "hopsets with constant hopbound and applications to approximate shortest paths":
    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 "distributed strong diameter network decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the use of randomness in local distributed graph algorithms")
  Member "a linear size logarithmic stretch path reporting distance oracle for general graphs":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on strong diameter padded decompositions")
  Member "very sparse additive spanners and emulators":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "lower bounds on sparse spanners emulators and diameter reducing shortcuts")
  Member "the 4 3 additive spanner exponent is tight":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "weighted additive spanners")
  Member "an entropy based proof for the moore bound for irregular graphs":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "set membership with a few bit probes")

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)