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 "approximating the nash social welfare with budget additive valuations"):
  Abstract: We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every $\varepsilon > 0$, our algorithm obtains a $(2.404 + \varepsilon)$-approximation in time polynomial in the input size and $1/\varepsilon$. #R##N#Our algorithm relies on rounding an approximate equilibrium in a linear Fisher market where sellers have earning limits (upper bounds on the amount of money they want to earn) and buyers have utility limits (upper bounds on the amount of utility they want to achieve). In contrast to markets with either earning or utility limits, these markets have not been studied before. They turn out to have fundamentally different properties. #R##N#Although the existence of equilibria is not guaranteed, we show that the market instances arising from the Nash social welfare problem always have an equilibrium. Further, we show that the set of equilibria is not convex, answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an approximate equilibrium. We show that the problem of computing an exact equilibrium lies in the intersection of classes PLS (Polynomial Local Search) and PPAD (Polynomial Parity Algorithms on Directed Graphs). For a constant number of buyers or goods, we give a polynomial-time algorithm to compute an exact equilibrium.

Includes members:
  Member "computing equilibria in markets with budget additive utilities":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the existence of pareto efficient and envy free allocations")
  Member "an improved combinatorial polynomial algorithm for the linear arrow debreu market":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "proportional dynamics in exchange economies")
  Member "apx hardness of maximizing nash social welfare with indivisible items":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "maximum nash welfare and other stories about efx")
  Member "an improved approximation guarantee for the maximum budgeted allocation problem":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "satiation in fisher markets and approximation of nash social welfare")
  Member "combinatorial walrasian equilibrium":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the power and limits of dynamic pricing in combinatorial markets")
  Member "a combinatorial polynomial algorithm for the linear arrow debreu market":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "proportional dynamics in exchange economies")
  Member "on allocating goods to maximize fairness":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "weighted completion time minimization for unrelated machines via iterative fair contention resolution")

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)