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 "a graphical transformation for belief propagation maximum weight matchings and odd sized cycles"):
  Abstract: We study the Maximum Weight Matching (MWM) problem for general graphs through the max-product Belief Propagation (BP) and related Linear Programming (LP). The BP approach provides distributed heuristics for finding the Maximum A Posteriori (MAP) assignment in a joint probability distribution represented by a Graphical Model (GM) and respective LPs can be considered as continuous relaxations of the discrete MAP problem. It was recently shown that a BP algorithm converges to the correct MWM assignment under a simple GM formulation of MAP/MWM as long as the corresponding LP relaxation is tight. First, under the motivation for forcing the tightness condition, we consider a new GM formulation of MWM, say C-GM, using non-intersecting odd-sized cycles in the graph: the new corresponding LP relaxation, say C-LP, becomes tight for more MWM instances. However, the tightness of C-LP now does not guarantee such convergence and correctness of the new BP on C-GM. To address the issue, we introduce a novel graph transformation applied to C-GM, which results in another GM formulation of MWM, and prove that the respective BP on it converges to the correct MAP/MWM assignment as long as C-LP is tight. Finally, we also show that C-LP always has half-integral solutions, which leads to an efficient BP-based MWM heuristic consisting of making sequential, `cutting plane', modifications to the underlying GM. Our experiments show that this BP-based cutting plane heuristic performs as well as that based on traditional LP solvers.

Includes members:
  Member "convergent message passing algorithms a unifying view":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "graph structured prediction energy networks")
  Member "on the optimality of tree reweighted max product message passing":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "partial optimality of dual decomposition for map inference in pairwise mrfs")
  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-3 (induced by source paper "pils exploring high order neighborhoods by pattern mining and injection")
  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")
  Member "max product for maximum weight matching convergence correctness and lp duality":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "my fair bandit distributed learning of max min fairness with multi player bandits")

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)