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 "optimal multi dimensional mechanism design reducing revenue to welfare maximization"):
  Abstract: We provide a reduction from revenue maximization to welfare maximization in multi-dimensional Bayesian auctions with arbitrary (possibly combinatorial) feasibility constraints and independent bidders with arbitrary (possibly combinatorial) demand constraints, appropriately extending Myerson's result to this setting. We also show that every feasible Bayesian auction can be implemented as a distribution over virtual VCG allocation rules. A virtual VCG allocation rule has the following simple form: Every bidder's type t_i is transformed into a virtual type f_i(t_i), via a bidder-specific function. Then, the allocation maximizing virtual welfare is chosen. Using this characterization, we show how to find and run the revenue-optimal auction given only black box access to an implementation of the VCG allocation rule. We generalize this result to arbitrarily correlated bidders, introducing the notion of a second-order VCG allocation rule. #R##N#We obtain our reduction from revenue to welfare optimization via two algorithmic results on reduced forms in settings with arbitrary feasibility and demand constraints. First, we provide a separation oracle for determining feasibility of a reduced form. Second, we provide a geometric algorithm to decompose any feasible reduced form into a distribution over virtual VCG allocation rules. In addition, we show how to execute both algorithms given only black box access to an implementation of the VCG allocation rule. #R##N#Our results are computationally efficient for all multi-dimensional settings where the bidders are additive. In this case, our mechanisms run in time polynomial in the total number of bidder types, but not type profiles. For generic correlated distributions, this is the natural description complexity of the problem. The runtime can be further improved to poly(#items, #bidders) in item-symmetric settings by making use of recent techniques.

Includes members:
  Member "bayesian optimal auctions via multi to single agent reduction":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a permutation equivariant neural network architecture for auction design")
  Member "matroid prophet inequalities":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "predict and match prophet inequalities with uncertain supply")
  Member "simple and nearly optimal multi item auctions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "optimal mechanisms for selling two items to a single buyer having uniformly distributed valuations")
  Member "bayesian combinatorial auctions expanding single buyer mechanisms to many buyers":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a permutation equivariant neural network architecture for auction design")
  Member "an algorithmic characterization of multi dimensional mechanisms":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a permutation equivariant neural network architecture for auction design")
  Member "extreme value theorems for optimal multidimensional pricing":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "escaping cannibalization correlation robust pricing for a unit demand buyer")
  Member "the power of randomness in bayesian optimal mechanism design":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "prophet inequalities with linear correlations and augmentations")
  Member "optimal auctions with correlated bidders are easy":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "lp based approximation for personalized reserve prices")

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.GT(Computer Science and Game Theory)