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 "message passing and combinatorial optimization"):
  Abstract: Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors. This thesis studies inference in discrete graphical models from an algebraic perspective and the ways inference can be used to express and approximate NP-hard combinatorial problems. #R##N#We investigate the complexity and reducibility of various inference problems, in part by organizing them in an inference hierarchy. We then investigate tractable approximations for a subset of these problems using distributive law in the form of message passing. The quality of the resulting message passing procedure, called Belief Propagation (BP), depends on the influence of loops in the graphical model. We contribute to three classes of approximations that improve BP for loopy graphs A) loop correction techniques; B) survey propagation, another message passing technique that surpasses BP in some settings; and C) hybrid methods that interpolate between deterministic message passing and Markov Chain Monte Carlo inference. #R##N#We then review the existing message passing solutions and provide novel graphical models and inference techniques for combinatorial problems under three broad classes: A) constraint satisfaction problems such as satisfiability, coloring, packing, set / clique-cover and dominating / independent set and their optimization counterparts; B) clustering problems such as hierarchical clustering, K-median, K-clustering, K-center and modularity optimization; C) problems over permutations including assignment, graph morphisms and alignment, finding symmetries and traveling salesman problem. In many cases we show that message passing is able to find solutions that are either near optimal or favourably compare with today's state-of-the-art approaches.

Includes members:
  Member "augmentative message passing for traveling salesman problem and graph partitioning":
    also connected through other hyperedges:
      (none)
  Member "perturbed message passing for constraint satisfaction problems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "learning variable ordering heuristics for solving constraint satisfaction problems")
  Member "revisiting algebra and complexity of inference in graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "perturbed message passing for constraint satisfaction problems")
  Member "on map inference by mwss on perfect graphs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "revisiting algebra and complexity of inference in graphical models")
  Member "loopy belief propagation for approximate inference an empirical study":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "analyzing differentiable fuzzy logic operators")
  Member "graphical models for game theory":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "message passing algorithms reparameterizations and splittings":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "decomposition bounds for marginal map")
  Member "the bethe permanent of a nonnegative matrix":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")

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.AI(Artificial Intelligence)