human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "improved bounds for reduction to depth 4 and depth 3"
  Abstract: Koiran showed that if a $n$-variate polynomial of degree $d$ (with $d=n^{O(1)}$) is computed by a circuit of size $s$, then it is also computed by a homogeneous circuit of depth four and of size $2^{O(\sqrt{d}\log(d)\log(s))}$. Using this result, Gupta, Kamath, Kayal and Saptharishi gave a $\exp(O(\sqrt{d\log(d)\log(n)\log(s)}))$ upper bound for the size of the smallest depth three circuit computing a $n$-variate polynomial of degree $d=n^{O(1)}$ given by a circuit of size $s$. #R##N#We improve here Koiran's bound. Indeed, we show that if we reduce an arithmetic circuit to depth four, then the size becomes $\exp(O(\sqrt{d\log(ds)\log(n)}))$. Mimicking Gupta, Kamath, Kayal and Saptharishi's proof, it also implies the same upper bound for depth three circuits. #R##N#This new bound is not far from optimal in the sense that Gupta, Kamath, Kayal and Saptharishi also showed a $2^{\Omega(\sqrt{d})}$ lower bound for the size of homogeneous depth four circuits such that gates at the bottom have fan-in at most $\sqrt{d}$. Finally, we show that this last lower bound also holds if the fan-in is at least $\sqrt{d}$.

Connected through hyperedge HE-1 (induced by source paper "lower bounds for matrix factorization"):
  with members:
    - "non malleable extractors and non malleable codes partially optimal constructions"
    - "static data structure lower bounds imply rigidity"
    - "matrix rigidity and the croot lev pach lemma"
    - "crossing the logarithmic barrier for dynamic boolean data structure lower bounds"
    - "probabilistic rank and matrix rigidity"
    - "hitting sets for roabp and sum of set multilinear circuits"
    - "on identity testing of tensors low rank recovery and compressed sensing"
    - "the cell probe complexity of dynamic range counting"

Connected through hyperedge HE-2 (induced by source paper "towards optimal depth reductions for syntactically multilinear circuits"):
  with members:
    - "an almost quadratic lower bound for syntactically multilinear arithmetic circuits"
    - "the chasm at depth four and tensor rank old results new insights"
    - "on the power of homogeneous depth 4 arithmetic circuits"
    - "arithmetic circuits the chasm at depth four gets wider"

Connected through hyperedge HE-3 (induced by source paper "lower bounds for multilinear bounded order abps"):
  with members:
    - "small depth multilinear formula lower bounds for iterated matrix multiplication with applications"
    - "some lower bound results for set multilinear arithmetic computations"

Connected through hyperedge HE-4 (induced by source paper "a near optimal depth hierarchy theorem for small depth multilinear circuits"):
  with members:
    - "small depth multilinear formula lower bounds for iterated matrix multiplication with applications"
    - "near optimal small depth lower bounds for small distance connectivity"
    - "an average case depth hierarchy theorem for boolean circuits"
    - "on the power of homogeneous depth 4 arithmetic circuits"
    - "arithmetic circuits the chasm at depth four gets wider"

Connected through hyperedge HE-5 (induced by source paper "succinct hitting sets and barriers to proving algebraic circuits lower bounds"):
  with members:
    - "towards an algebraic natural proofs barrier via polynomial identity testing"
    - "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"
    - "proof complexity lower bounds from algebraic circuit complexity"
    - "bipartite perfect matching is in quasi nc"
    - "boundaries of vp and vnp"
    - "unifying known lower bounds via geometric complexity theory"
    - "progress on polynomial identity testing ii"
    - "subexponential size hitting sets for bounded depth multilinear formulas"

Connected through hyperedge HE-6 (induced by source paper "towards an algebraic natural proofs barrier via polynomial identity testing"):
  with members:
    - "succinct hitting sets and barriers to proving algebraic circuits lower bounds"
    - "arithmetic circuits with locally low algebraic rank"
    - "geometric complexity theory and matrix powering"
    - "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"
    - "no occurrence obstructions in geometric complexity theory"
    - "the chasm at depth four and tensor rank old results new insights"
    - "on minimal free resolutions and the method of shifted partial derivatives in complexity theory"
    - "rectangular kronecker coefficients and plethysms in geometric complexity theory"

Connected through hyperedge HE-7 (induced by source paper "on algebraic branching programs of small width"):
  with members:
    - "the complexity of factors of multivariate polynomials"
    - "succinct hitting sets and barriers to proving algebraic circuits lower bounds"
    - "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"
    - "no occurrence obstructions in geometric complexity theory"
    - "a 2n 2 log n 1 lower bound for the border rank of matrix multiplication"
    - "boundaries of vp and vnp"
    - "unifying known lower bounds via geometric complexity theory"
    - "a lower bound for the determinantal complexity of a hypersurface"

Connected through hyperedge HE-8 (induced by source paper "arithmetic circuits with locally low algebraic rank"):
  with members:
    - "an exponential lower bound for homogeneous depth 5 circuits over finite fields"
    - "sums of products of polynomials in few variables lower bounds and polynomial identity testing"
    - "subexponential size hitting sets for bounded depth multilinear formulas"
    - "on the power of homogeneous depth 4 arithmetic circuits"
    - "the limits of depth reduction for arithmetic formulas it s all about the top fan in"
    - "quasipolynomial time identity testing of non commutative and read once oblivious algebraic branching programs"
    - "jacobian hits circuits hitting sets lower bounds for depth d occur k formulas depth 3 transcendence degree k circuits"
    - "algebraic independence and blackbox identity testing"

Question: Please tell me which class the center node 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.CC(Computational Complexity)