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 "constraint complexity of realizations of linear codes on arbitrary graphs"):
  Abstract: A graphical realization of a linear code C consists of an assignment of the coordinates of C to the vertices of a graph, along with a specification of linear state spaces and linear "local constraint" codes to be associated with the edges and vertices, respectively, of the graph. The kappa-complexity of a graphical realization is defined to be the largest dimension of any of its local constraint codes, kappa -complexity is a reasonable measure of the computational complexity of a sum-product decoding algorithm specified by a graphical realization. The main focus of this paper is on the following problem: given a linear code C and a graph G, how small can the kappa-complexity of a realization of C on G be? As useful tools for attacking this problem, we introduce the vertex-cut bound, and the notion of "vc-treewidth" for a graph, which is closely related to the well-known graph-theoretic notion of treewidth. Using these tools, we derive tight lower bounds on the kappa-complexity of any realization of C on G. Our bounds enable us to conclude that good error-correcting codes can have low-complexity realizations only on graphs with large vc-treewidth. Along the way, we also prove the interesting result that the ratio of the kappa-complexity of the best conventional trellis realization of a length-n code C to the kappa-complexity of the best cycle-free realization of C grows at most logarithmically with code length n. Such a logarithmic growth rate is, in fact, achievable.

Includes members:
  Member "on minimal tree realizations of linear codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "codes on graphs observability controllability and local reducibility")
  Member "the extraction and complexity limits of graphical models for linear codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on pseudocodewords and decision regions of linear programming decoding of hdpc codes")

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.DM(Discrete Mathematics)