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 index coding via graph homomorphism"):
  Abstract: It is known that the minimum broadcast rate of a linear index code over $\mathbb{F}_q$ is equal to the $minrank_q$ of the underlying digraph. In [3] it is proved that for $\mathbb{F}_2$ and any positive integer $k$, $minrank_q(G)\leq k$ iff there exists a homomorphism from the complement of the graph $G$ to the complement of a particular undirected graph family called "graph family $\{G_k\}$". As observed in [2], by combining these two results one can relate the linear index coding problem of undirected graphs to the graph homomorphism problem. In [4], a direct connection between linear index coding problem and graph homomorphism problem is introduced. In contrast to the former approach, the direct connection holds for digraphs as well and applies to any field size. More precisely, in [4], a graph family $\{H_k^q\}$ is introduced and shown that whether or not the scalar linear index of a digraph $G$ is less than or equal to $k$ is equivalent to the existence of a graph homomorphism from the complement of $G$ to the complement of $H_k^q$. #R##N#Here, we first study the structure of the digraphs $H_k^q$. Analogous to the result of [2] about undirected graphs, we prove that $H_k^q$'s are vertex transitive digraphs. Using this, and by applying a lemma of Hell and Nesetril [5], we derive a class of necessary conditions for digraphs $G$ to satisfy $lind_q(G)\leq k$. Particularly, we obtain new lower bounds on $lind_q(G)$. #R##N#Our next result is about the computational complexity of scalar linear index of a digraph. It is known that deciding whether the scalar linear index of an undirected graph is equal to $k$ or not is NP-complete for $k\ge 3$ and is polynomially decidable for $k=1,2$ [3]. For digraphs, it is shown in [6] that for the binary alphabet, the decision problem for $k=2$ is NP-complete. We use graph homomorphism framework to extend this result to arbitrary alphabet.

Includes members:
  Member "on index coding and graph homomorphism":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "index coding rank invariant extensions")
  Member "on the capacity region for index coding":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "an index coding approach to caching with uncoded cache placement")
  Member "local graph coloring and index coding":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "embedded index coding")
  Member "an equivalence between network coding and index coding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "embedded index coding")
  Member "index coding an interference alignment perspective":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "conditional disclosure of secrets a noise and signal alignment approach")
  Member "optimal index codes with near extreme rates":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "an optimal linear error correcting delivery scheme for coded caching with shared caches")
  Member "on linear index coding for random graphs":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "index codes with minimum locality for three receiver unicast problems")
  Member "linear index coding via semidefinite programming":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "the generalized orthogonality dimension of generalized kneser graphs bounds and applications")

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)