human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "on an extremal hypergraph problem related to combinatorial batch codes"
  Abstract: Let $n, r, k$ be positive integers such that $3\leq k < n$ and $2\leq r \leq k-1$. Let $m(n, r, k)$ denote the maximum number of edges an $r$-uniform hypergraph on $n$ vertices can have under the condition that any collection of $i$ edges, span at least $i$ vertices for all $1 \leq i \leq k$. We are interested in the asymptotic nature of $m(n, r, k)$ for fixed $r$ and $k$ as $n \rightarrow \infty$. This problem is related to the forbidden hypergraph problem introduced by Brown, Erd\H{o}s, and S\'os and very recently discussed in the context of combinatorial batch codes. In this short paper we obtain the following results. {enumerate}[(i)] Using a result due to Erd\H{o}s we are able to show $m(n, k, r) = o(n^r)$ for $7\leq k$, and $3 \leq r \leq k-1-\lceil\log k \rceil$. This result is best possible with respect to the upper bound on $r$ as we subsequently show through explicit construction that for $6 \leq k$, and $k-\lceil \log k \rceil \leq r \leq k-1, m(n, r, k) = \Theta(n^r)$. #R##N#This explicit construction improves on the non-constructive general lower bound obtained by Brown, Erd\H{o}s, and S\'os for the considered parameter values. For 2-uniform CBCs we obtain the following results. {enumerate} We provide exact value of $m(n, 2, 5)$ for $n \geq 5$. Using a result of Lazebnik,et al. regarding maximum size of graphs with large girth, we improve the existing lower bound on $m(n, 2, k)$ ($\Omega(n^{\frac{k+1}{k-1}})$) for all $k \geq 8$ and infinitely many values of $n$. We show $m(n, 2, k) = O(n^{1+\frac{1}{\lfloor\frac{k}{4}\rfloor}})$ by using a result due to Bondy and Simonovits, and also show $m(n, 2, k) = \Theta(n^{3/2})$ for $k = 6, 7, 8$ by using a result of K\"{o}vari, S\'os, and Tur\'{a}n.

Connected through hyperedge HE-1 (induced by source paper "multiset combinatorial batch codes"):
  with members:
    - "bounds and constructions of codes with multiple localities"
    - "fractional repetition and erasure batch codes"
    - "locality and availability in distributed storage"
    - "optimal combinatorial batch codes based on block designs"
    - "combinatorial batch codes a lower bound and optimal constructions"

Connected through hyperedge HE-2 (induced by source paper "derandomized construction of combinatorial batch codes"):
  with members:
    - "optimal combinatorial batch codes based on block designs"
    - "combinatorial batch codes a lower bound and optimal constructions"

Connected through hyperedge HE-3 (induced by source paper "optimal fractional repetition codes based on graphs and designs"):
  with members:
    - "fractional repetition and erasure batch codes"
    - "fractional repetition codes with flexible repair from combinatorial designs"
    - "optimal combinatorial batch codes based on block designs"
    - "zigzag codes mds array codes with optimal rebuilding"
    - "reconstruction and repair degree of fractional repetition codes"
    - "replication based storage systems with local repair"
    - "locally repairable codes with multiple repair alternatives"
    - "exact repair regenerating codes via layered erasure correction and block designs"

Connected through hyperedge HE-4 (induced by source paper "batch codes through dense graphs without short cycles"):
  with members:
    - "locality and availability in distributed storage"
    - "optimal locally repairable and secure codes for distributed storage systems"
    - "linear batch codes"
    - "a family of optimal locally recoverable codes"
    - "optimal combinatorial batch codes based on block designs"
    - "xoring elephants novel erasure codes for big data"
    - "local correctability of expander codes"
    - "zigzag codes mds array codes with optimal rebuilding"

Connected through hyperedge HE-5 (induced by source paper "optimal combinatorial batch codes based on block designs"):
  with members:
    - "combinatorial batch codes a lower bound and optimal constructions"
    - "more on combinatorial batch codes"

Question: Please tell me which class the center node 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)