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 "plantinga vegter algorithm takes average polynomial time"):
  Abstract: We exhibit a condition-based analysis of the adaptive subdivision algorithm due to Plantinga and Vegter. The first complexity analysis of the \pv~Algorithm is due to Burr, Gao and Tsigaridas who proved a \mathcalO \big(2^τ d^4 log d \big) worst-case cost bound for degree d plane curves with maximum coefficient bit-size~τ. This exponential bound, it was observed, is in stark contrast with the good performance of the algorithm in practice. More in line with this performance, we show that, with respect to a broad family of measures, the expected time complexity of the \pv~Algorithm is bounded by O(d^7) for real, degree d, plane curves. We also exhibit a smoothed analysis of the \pv~Algorithm that yields similar complexity estimates. To obtain these results we combine robust probabilistic techniques coming from geometric functional analysis with condition numbers and the continuous amortization paradigm introduced by Burr, Krahmer and Yap. We hope this will motivate a fruitful exchange of ideas between the different approaches to numerical computation.

Includes members:
  Member "computing the homology of semialgebraic sets i lax formulas":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "computing the homology of semialgebraic sets ii general formulas")
  Member "computing the homology of basic semialgebraic sets in weak exponential time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "smooth points on semi algebraic sets")
  Member "the complexity of subdivision for diameter distance tests":
    also connected through other hyperedges:
      (none)
  Member "a numerical algorithm for zero counting ii distance to ill posedness and smoothed analysis":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "computing the homology of semialgebraic sets i lax formulas")
  Member "a numerical algorithm for zero counting i complexity and accuracy":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "new progress in univariate polynomial root finding")

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.CG(Computational Geometry)