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: "convex program duality fisher markets and nash social welfare"
  Abstract: We study Fisher markets and the problem of maximizing the Nash social welfare (NSW), and show several closely related new results. In particular, we obtain: #R##N#-- A new integer program for the NSW maximization problem whose fractional relaxation has a bounded integrality gap. In contrast, the natural integer program has an unbounded integrality gap. #R##N#-- An improved, and tight, factor 2 analysis of the algorithm of [7]; in turn showing that the integrality gap of the above relaxation is at most 2. The approximation factor shown by [7] was $2e^{1/e} \approx 2.89$. #R##N#-- A lower bound of $e^{1/e}\approx 1.44$ on the integrality gap of this relaxation. #R##N#-- New convex programs for natural generalizations of linear Fisher markets and proofs that these markets admit rational equilibria. #R##N#These results were obtained by establishing connections between previously known disparate results, and they help uncover their mathematical underpinnings. We show a formal connection between the convex programs of Eisenberg and Gale and that of Shmyrev, namely that their duals are equivalent up to a change of variables. Both programs capture equilibria of linear Fisher markets. By adding suitable constraints to Shmyrev's program, we obtain a convex program that captures equilibria of the spending-restricted market model defined by [7] in the context of the NSW maximization problem. Further, adding certain integral constraints to this program we get the integer program for the NSW mentioned above. #R##N#The basic tool we use is convex programming duality. In the special case of convex programs with linear constraints (but convex objectives), we show a particularly simple way of obtaining dual programs, putting it almost at par with linear program duality. This simple way of finding duals has been used subsequently for many other applications.

Connected through hyperedge HE-1 (induced by source paper "maximum nash welfare and other stories about efx"):
  with members:
    - "envy freeness up to any item with high nash welfare the virtue of donating items"
    - "almost envy freeness in group resource allocation"
    - "approximating nash social welfare under submodular valuations through un matchings"
    - "maximin aware allocations of indivisible goods"
    - "greedy algorithms for fair division of mixed manna"
    - "an improved approximation algorithm for maximin shares"
    - "greedy algorithms for maximizing nash social welfare"
    - "groupwise maximin fair allocation of indivisible goods"

Connected through hyperedge HE-2 (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-3 (induced by source paper "algorithms for competitive division of chores"):
  with members:
    - "fair division with minimal sharing"
    - "strategyproof and approximately maxmin fair share allocation of chores"
    - "universal growth in production economies"
    - "fair allocation of combinations of indivisible goods and chores"
    - "on the proximity of markets with integral equilibria"
    - "competitive division of a mixed manna"
    - "approximation algorithms for computing maximin share allocations"
    - "almost envy freeness with general valuations"

Connected through hyperedge HE-4 (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"
    - "nash social welfare for indivisible items under separable piecewise linear concave utilities"

Connected through hyperedge HE-5 (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"
    - "nash social welfare for indivisible items under separable piecewise linear concave utilities"
    - "nash social welfare matrix permanent and stable polynomials"
    - "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-6 (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"
    - "nash social welfare for indivisible items under separable piecewise linear concave utilities"
    - "nash social welfare matrix permanent and stable polynomials"
    - "apx hardness of maximizing nash social welfare with indivisible items"
    - "combinatorial algorithm for restricted max min fair allocation"

Connected through hyperedge HE-7 (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-8 (induced by source paper "on the existence of pareto efficient and envy free allocations"):
  with members:
    - "near optimal communication lower bounds for approximate nash equilibria"
    - "communication complexity of cake cutting"
    - "almost envy freeness with general valuations"
    - "approximating the nash social welfare with budget additive valuations"
    - "communication complexity of discrete fair division"
    - "computing equilibria in markets with budget additive utilities"
    - "nash social welfare for indivisible items under separable piecewise linear concave utilities"
    - "communication complexity of approximate nash equilibria"

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.GT(Computer Science and Game Theory)