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 "bilu linial stability certified algorithms and the independent set problem"):
  Abstract: We study the notion of Bilu-Linial stability in the context of Independent Set. A weighted instance $G=(V,E,w)$ of Independent Set is $\gamma$-stable if it has a unique optimal solution that remains the unique optimal solution under multiplicative perturbations of the weights by a factor of at most $\gamma\geq 1$. In this work, we use the standard LP as well as the Sherali-Adams hierarchy to design algorithms for $(\Delta-1)$-stable instances on graphs of maximum degree $\Delta$, for $(k-1)$-stable instances on $k$-colorable graphs and for $(1+\varepsilon)$-stable instances on planar graphs. We also show that the integrality gap of relaxations of several maximization problems reduces dramatically on stable instances. For general graphs we give an algorithm for $(\varepsilon n)$-stable instances (for fixed $\varepsilon>0$), and on the negative side we show that there are no efficient algorithms for $O(n^{\frac{1}{2}-\varepsilon})$-stable instances assuming the planted clique conjecture. As a side note, we exploit the connection between Vertex Cover and Node Multiway Cut and give the first results about stable instances of Node Multiway Cut. #R##N#Moreover, we initiate the study of certified algorithms for Independent Set. The class of $\gamma$-certified algorithms is a class of $\gamma$-approximation algorithms introduced by Makarychev and Makarychev (2018) whose returned solution is optimal for a perturbation of the original instance. Using results of Makarychev and Makarychev (2018) as well as combinatorial techniques, we obtain $\Delta$-certified algorithms for Independent Set on graphs of maximum degree $\Delta$ and $(1+\varepsilon)$-certified algorithms on planar graphs. Finally, we prove that an algorithm of Berman and F\"{u}rer (1994) is a $\left(\frac{\Delta+1}{3}+\varepsilon\right)$-certified algorithm on graphs of maximum degree $\Delta$ where all weights are equal to 1.

Includes members:
  Member "on euclidean k means clustering with alpha center proximity":
    also connected through other hyperedges:
      (none)
  Member "exact algorithms and lower bounds for stable instances of euclidean k means":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "graph pricing with limited supply")
  Member "perturbation resilient clustering for k center and related problems via lp relaxations":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "robust communication optimal distributed clustering algorithms")
  Member "stability and recovery for independence systems":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the unreasonable effectiveness of the greedy algorithm greedy adapts to sharpness")
  Member "lp based robust algorithms for noisy minor free and bounded treewidth graphs":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "covering vectors by spaces in perturbed graphic matroids and their duals")
  Member "k center clustering under perturbation resilience":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "semi bandit optimization in the dispersed setting")
  Member "on the lov asz theta function for independent sets in sparse graphs":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "simple and local independent set approximation")
  Member "sum of squares lower bounds for planted clique":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators")

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)