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 "complexity of a root clustering algorithm"):
  Abstract: Approximating the roots of a holomorphic function in an input box is a fundamental problem in many domains. Most algorithms in the literature for solving this problem are conditional, i.e., they make some simplifying assumptions, such as, all the roots are simple or there are no roots on the boundary of the input box, or the underlying machine model is Real RAM. Root clustering is a generalization of the root approximation problem that allows for errors in the computation and makes no assumption on the multiplicity of the roots. An unconditional algorithm for computing a root clustering of a holomorphic function was given by Yap, Sagraloff and Sharma in 2013. They proposed a subdivision based algorithm using effective predicates based on Pellet's test while avoiding any comparison with zeros (using soft zero comparisons instead). In this paper, we analyze the running time of their algorithm. We use the continuous amortization framework to derive an upper bound on the size of the subdivision tree. We specialize this bound to the case of polynomials and some simple transcendental functions such as exponential and trigonometric sine. We show that the algorithm takes exponential time even for these simple functions, unlike the case of polynomials. We also derive a bound on the bit-precision used by the algorithm. To the best of our knowledge, this is the first such result for holomorphic functions. We introduce new geometric parameters, such as the relative growth of the function on the input box, for analyzing the algorithm. Thus, our estimates naturally generalize the known results, i.e., for the case of polynomials.

Includes members:
  Member "arb efficient arbitrary precision midpoint radius interval arithmetic":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "fungrim a symbolic library for special functions")
  Member "a near optimal subdivision algorithm for complex root isolation based on the pellet test and newton iteration":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "new progress in univariate polynomial root finding")
  Member "on the complexity of solving a bivariate polynomial system":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the complexity of computing the topology of real algebraic space curves")

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)