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 "linear network coding linear index coding and representable discrete polymatroids"):
  Abstract: Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections among linear network coding, linear index coding and representable discrete polymatroids. We consider vector linear solutions of networks over a field $\mathbb{F}_q,$ with possibly different message and edge vector dimensions, which are referred to as linear fractional solutions. We define a \textit{discrete polymatroidal} network and show that a linear fractional solution over a field $\mathbb{F}_q,$ exists for a network if and only if the network is discrete polymatroidal with respect to a discrete polymatroid representable over $\mathbb{F}_q.$ An algorithm to construct networks starting from certain class of discrete polymatroids is provided. Every representation over $\mathbb{F}_q$ for the discrete polymatroid, results in a linear fractional solution over $\mathbb{F}_q$ for the constructed network. Next, we consider the index coding problem and show that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions which are determined by the index coding problem considered. El Rouayheb et. al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a \textit{perfect linear index coding solution} for an index coding problem obtained from that matroid. We generalize the result of El Rouayheb et. al. by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid.

Includes members:
  Member "achievable rate regions for network coding":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "characteristic dependent linear rank inequalities via complementary vector spaces")
  Member "an equivalence between network coding and index coding":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "embedded index coding")
  Member "a matroidal framework for network error correcting codes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "optimal locally repairable codes and connections to matroid theory")
  Member "computing bounds on network capacity regions as a polytope reconstruction problem":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a linear network code construction for general integer connections based on the constraint satisfaction problem")
  Member "scalar linear solvability of matroidal networks associated with representable matroids":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "multicast networks solvable over every finite field")
  Member "on the index coding problem and its relation to network coding and matroid theory":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "efficient 3d road map data exchange for intelligent vehicles in vehicular fog networks")

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.IT(Information Theory)