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: "extended formulations non negative factorizations and randomized communication protocols"
  Abstract: An extended formulation of a polyhedron $P$ is a linear description of a polyhedron $Q$ together with a linear map $\pi$ such that $\pi(Q)=P$. These objects are of fundamental importance in polyhedral combinatorics and optimization theory, and the subject of a number of studies. Yannakakis' factorization theorem [M. Yannakakis. Expressing combinatorial optimization problems by linear programs. {\em J. Comput. System Sci.}, 43(3):441--466 (1991)] provides a surprising connection between extended formulations and communication complexity, showing that the smallest size of an extended formulation of $P$ equals the nonnegative rank of its slack matrix $S$. Moreover, Yannakakis also shows that the nonnegative rank of $S$ is at most $2^c$, where $c$ is the complexity of any \emph{deterministic} protocol computing $S$. In this paper, we show that the latter result can be strengthened when we allow protocols to be \emph{randomized}. In particular, we prove that the base-2 logarithm of the nonnegative rank of any nonnegative matrix equals the minimum complexity of a randomized communication protocol computing the matrix in expectation. Using Yannakakis' factorization theorem, this implies that the base-2 logarithm of the smallest size of an extended formulation of a polytope $P$ equals the minimum complexity of a randomized communication protocol computing the slack matrix of $P$ in expectation. We show that allowing randomization in the protocol can be crucial for obtaining small extended formulations. Specifically, we prove that for the spanning tree and perfect matching polytopes, small variance in the protocol forces large size in the extended formulation.

Connected through hyperedge HE-1 (induced by source paper "on the combinatorial lower bound for the extension complexity of the spanning tree polytope"):
  with members:
    - "fooling sets and the spanning tree polytope"
    - "the minimum rank of typical fooling set matrices"
    - "the matching polytope has exponential extension complexity"

Connected through hyperedge HE-2 (induced by source paper "fooling sets and the spanning tree polytope"):
  with members:
    - "on the combinatorial lower bound for the extension complexity of the spanning tree polytope"
    - "the minimum rank of typical fooling set matrices"

Connected through hyperedge HE-3 (induced by source paper "the matching polytope does not admit fully polynomial size relaxation schemes"):
  with members:
    - "average case polyhedral complexity of the maximum stable set problem"
    - "affine reductions for lps and sdps"
    - "lower bounds on the size of semidefinite programming relaxations"
    - "exponential lower bounds on the size of approximate formulations in the natural encoding for capacitated facility location"
    - "approximate constraint satisfaction requires large lp relaxations"
    - "on the existence of 0 1 polytopes with high semidefinite extension complexity"
    - "the matching polytope has exponential extension complexity"
    - "approximation limits of linear programs beyond hierarchies"

Connected through hyperedge HE-4 (induced by source paper "some upper and lower bounds on psd rank"):
  with members:
    - "lower bounds on the size of semidefinite programming relaxations"
    - "the square root rank of the correlation polytope is exponential"
    - "the matching polytope has exponential extension complexity"

Connected through hyperedge HE-5 (induced by source paper "a generalization of extension complexity that captures p"):
  with members:
    - "the matching polytope has exponential extension complexity"

Connected through hyperedge HE-6 (induced by source paper "approximate constraint satisfaction requires large lp relaxations"):
  with members:
    - "the matching problem has no small symmetric sdp"
    - "lower bounds on the size of semidefinite programming relaxations"
    - "the matching polytope has exponential extension complexity"
    - "approximation limits of linear programs beyond hierarchies"
    - "an entropic proof of chang s inequality"
    - "max cut and the smallest eigenvalue"

Connected through hyperedge HE-7 (induced by source paper "the matching polytope has exponential extension complexity"):
  with members:
    - "the matching polytope does not admit fully polynomial size relaxation schemes"
    - "lower bounds on the size of semidefinite programming relaxations"
    - "approximate constraint satisfaction requires large lp relaxations"
    - "on the existence of 0 1 polytopes with high semidefinite extension complexity"
    - "approximation limits of linear programs beyond hierarchies"
    - "extended formulations for polygons"

Connected through hyperedge HE-8 (induced by source paper "on the existence of 0 1 polytopes with high semidefinite extension complexity"):
  with members:
    - "the matching polytope has exponential extension complexity"
    - "approximation limits of linear programs beyond hierarchies"
    - "extended formulations for polygons"

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.DM(Discrete Mathematics)