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 "everywhere sparse spanners via dense subgraphs"):
  Abstract: The significant progress in constructing graph spanners that are sparse (small number of edges) or light (low total weight) has skipped spanners that are everywhere-sparse (small maximum degree). This disparity is in line with other network design problems, where the maximum-degree objective has been a notorious technical challenge. Our main result is for the Lowest Degree 2-Spanner (LD2S) problem, where the goal is to compute a 2-spanner of an input graph so as to minimize the maximum degree. We design a polynomial-time algorithm achieving approximation factor $\tilde O(\Delta^{3-2\sqrt{2}}) \approx \tilde O(\Delta^{0.172})$, where $\Delta$ is the maximum degree of the input graph. The previous $\tilde O(\Delta^{1/4})$ -approximation was proved nearly two decades ago by Kortsarz and Peleg [SODA 1994, SICOMP 1998]. #R##N#Our main conceptual contribution is to establish a formal connection between LD2S and a variant of the Densest k-Subgraph (DkS) problem. Specifically, we design for both problems strong relaxations based on the Sherali-Adams linear programming (LP) hierarchy, and show that "faithful" randomized rounding of the DkS-variant can be used to round LD2S solutions. Our notion of faithfulness intuitively means that all vertices and edges are chosen with probability proportional to their LP value, but the precise formulation is more subtle. #R##N#Unfortunately, the best algorithms known for DkS use the Lov\'asz-Schrijver LP hierarchy in a non-faithful way [Bhaskara, Charikar, Chlamtac, Feige, and Vijayaraghavan, STOC 2010]. Our main technical contribution is to overcome this shortcoming, while still matching the gap that arises in random graphs by planting a subgraph with same log-density.

Includes members:
  Member "fault tolerant spanners better and simpler":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "approximate distance oracles subject to multiple vertex failures")
  Member "approximating sparsest cut in graphs of bounded treewidth":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "integrality gaps for bounded color matchings")
  Member "improved approximation for the directed spanner problem":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a fast network decomposition algorithm and its applications to constant time distributed computation")
  Member "dial a ride from k forest":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "reachability preservers new extremal bounds and approximation algorithms")
  Member "lower stretch spanning trees":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "2 node connectivity network design")
  Member "nearly linear time algorithms for graph partitioning graph sparsification and solving linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "compressive sensing for cut improvement and local clustering")

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)