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 "belief propagation for linear programming"):
  Abstract: Belief Propagation (BP) is a popular, distributed heuristic for performing MAP computations in Graphical Models. BP can be interpreted, from a variational perspective, as minimizing the Bethe Free Energy (BFE). BP can also be used to solve a special class of Linear Programming (LP) problems. For this class of problems, MAP inference can be stated as an integer LP with an LP relaxation that coincides with minimization of the BFE at ``zero temperature". We generalize these prior results and establish a tight characterization of the LP problems that can be formulated as an equivalent LP relaxation of MAP inference. Moreover, we suggest an efficient, iterative annealing BP algorithm for solving this broader class of LP problems. We demonstrate the algorithm's performance on a set of weighted matching problems by using it as a cutting plane method to solve a sequence of LPs tightened by adding ``blossom'' inequalities.

Includes members:
  Member "the cutting plane method is polynomial for perfect matchings":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "minimum weight perfect matching via blossom belief propagation")
  Member "map estimation linear programming and belief propagation with convex free energies":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "convergence rates of smooth message passing with rounding in entropy regularized map inference")
  Member "improved linear programming decoding using frustrated cycles":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "graphical models and belief propagation hierarchy for physics constrained network flows")
  Member "belief propagation for min cost network flow convergence and correctness":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "react reactive resilience for critical infrastructures using graph coloring techniques")
  Member "message passing for maximum weight independent set":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "throughput optimal decentralized scheduling with single bit state feedback for a class of queueing systems")
  Member "max product for maximum weight matching convergence correctness and lp duality":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "my fair bandit distributed learning of max min fairness with multi player bandits")
  Member "guessing facets polytope structure and improved lp decoder":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "mathematical programming decoding of binary linear codes theory and algorithms")
  Member "adaptive methods for linear programming decoding":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "efficient qp admm decoder for binary ldpc codes and its performance analysis")

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)