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 "max product belief propagation for linear programming applications to combinatorial optimization"):
  Abstract: Max-product belief propagation (BP) is a popular message-passing algorithm for computing a maximum-a-posteriori (MAP) assignment in a joint distribution represented by a graphical model (GM). It has been shown that BP can solve a few classes of Linear Programming (LP) formulations to combinatorial optimization problems including maximum weight matching and shortest path, i.e., BP can be a distributed solver for certain LPs. However, those LPs and corresponding BP analysis are very sensitive to underlying problem setups, and it has been not clear what extent these results can be generalized to. In this paper, we obtain a generic criteria that BP converges to the optimal solution of given LP, and show that it is satisfied in LP formulations associated to many classical combinatorial optimization problems including maximum weight perfect matching, shortest path, traveling salesman, cycle packing and vertex cover. More importantly, our criteria can guide the BP design to compute fractional LP solutions, while most prior results focus on integral ones. Our results provide new tools on BP analysis and new directions on efficient solvers for large-scale LPs.

Includes members:
  Member "a graphical transformation for belief propagation maximum weight matchings and odd sized cycles":
    also connected through other hyperedges:
      (none)
  Member "complexity of inference in graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "worst case polynomial time exact map inference on discrete models with global dependencies")
  Member "belief propagation for weighted b matchings on arbitrary graphs and its relation to linear programs with integer solutions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "pils exploring high order neighborhoods by pattern mining and injection")
  Member "graphlab a new framework for parallel machine learning":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "relaxed scheduling for scalable belief propagation")
  Member "message passing for maximum weight independent set":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "throughput optimal decentralized scheduling with single bit state feedback for a class of queueing systems")

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)