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: "nash social welfare matrix permanent and stable polynomials"
  Abstract: We study the problem of allocating $m$ items to $n$ agents subject to maximizing the Nash social welfare (NSW) objective. We write a novel convex programming relaxation for this problem, and we show that a simple randomized rounding algorithm gives a $1/e$ approximation factor of the objective. #R##N#Our main technical contribution is an extension of Gurvits's lower bound on the coefficient of the square-free monomial of a degree $m$-homogeneous stable polynomial on $m$ variables to all homogeneous polynomials. We use this extension to analyze the expected welfare of the allocation returned by our randomized rounding algorithm.

Connected through hyperedge HE-1 (induced by source paper "efx exists for three agents"):
  with members:
    - "envy freeness up to any item with high nash welfare the virtue of donating items"
    - "approximating nash social welfare under submodular valuations through un matchings"
    - "a little charity guarantees almost envy freeness"
    - "an improved approximation algorithm for maximin shares"
    - "on fair division of indivisible items"
    - "almost envy freeness with general valuations"
    - "approximating the nash social welfare with budget additive valuations"
    - "finding fair and efficient allocations"

Connected through hyperedge HE-2 (induced by source paper "envy freeness up to any item with high nash welfare the virtue of donating items"):
  with members:
    - "comparing approximate relaxations of envy freeness"
    - "on fair division of indivisible items"
    - "approximation algorithms for computing maximin share allocations"
    - "almost envy freeness with general valuations"
    - "approximating the nash social welfare with budget additive valuations"
    - "finding fair and efficient allocations"
    - "a discrete and bounded envy free cake cutting protocol for any number of agents"
    - "convex program duality fisher markets and nash social welfare"

Connected through hyperedge HE-3 (induced by source paper "satiation in fisher markets and approximation of nash social welfare"):
  with members:
    - "near optimal online algorithms and fast approximation algorithms for resource allocation problems"
    - "a strongly polynomial algorithm for linear exchange markets"
    - "approximating the nash social welfare with budget additive valuations"
    - "finding fair and efficient allocations"
    - "convex program duality fisher markets and nash social welfare"
    - "nash social welfare for indivisible items under separable piecewise linear concave utilities"
    - "an improved combinatorial polynomial algorithm for the linear arrow debreu market"
    - "apx hardness of maximizing nash social welfare with indivisible items"

Connected through hyperedge HE-4 (induced by source paper "approximating nash social welfare under submodular valuations through un matchings"):
  with members:
    - "on fair division of indivisible items"
    - "a tale of santa claus hypergraphs and matroids"
    - "approximating the nash social welfare with budget additive valuations"
    - "finding fair and efficient allocations"
    - "convex program duality fisher markets and nash social welfare"
    - "nash social welfare for indivisible items under separable piecewise linear concave utilities"
    - "apx hardness of maximizing nash social welfare with indivisible items"
    - "combinatorial algorithm for restricted max min fair allocation"

Connected through hyperedge HE-5 (induced by source paper "a little charity guarantees almost envy freeness"):
  with members:
    - "envy freeness up to any item with high nash welfare the virtue of donating items"
    - "an improved approximation algorithm for maximin shares"
    - "almost envy free allocations with connected bundles"
    - "on fair division of indivisible items"
    - "groupwise maximin fair allocation of indivisible goods"
    - "almost envy freeness with general valuations"
    - "approximating the nash social welfare with budget additive valuations"
    - "finding fair and efficient allocations"

Connected through hyperedge HE-6 (induced by source paper "auction algorithms for market equilibrium with weak gross substitute demands"):
  with members:
    - "on fair division of indivisible items"
    - "finding fair and efficient allocations"
    - "convex program duality fisher markets and nash social welfare"
    - "nash social welfare for indivisible items under separable piecewise linear concave utilities"
    - "ascending price algorithms for unknown markets"
    - "convergence of tâtonnement in fisher markets"
    - "tatonnement in ongoing markets of complementary goods"
    - "a combinatorial polynomial algorithm for the linear arrow debreu market"

Connected through hyperedge HE-7 (induced by source paper "waring rank parameterized and exact algorithms"):
  with members:
    - "fast exact algorithms using hadamard product of polynomials"
    - "extensor coding"
    - "barriers for rank methods in arithmetic complexity"
    - "designing deterministic polynomial space algorithms by color coding multivariate polynomials"
    - "the border support rank of two by two matrix multiplication is seven"
    - "no occurrence obstructions in geometric complexity theory"
    - "graph isomorphism in quasipolynomial time"
    - "finding and counting vertex colored subtrees"

Connected through hyperedge HE-8 (induced by source paper "a tight analysis of bethe approximation for permanent"):
  with members:
    - "log concave polynomials i entropy and a deterministic approximation algorithm for counting bases of matroids"
    - "approximate profile maximum likelihood"
    - "belief propagation bethe approximation and polynomials"
    - "approximating the permanent of a random matrix with vanishing mean"
    - "a generalization of permanent inequalities and applications in counting and optimization"
    - "the bethe permanent of a nonnegative matrix"
    - "approximating the permanent with fractional belief propagation"
    - "approximating the permanent with belief propagation"

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.DS(Data Structures and Algorithms)