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 "locally repairable codes with multiple r_ i delta_ i localities"):
  Abstract: In distributed storage systems, locally repairable codes (LRCs) are introduced to realize low disk I/O and repair cost. In order to tolerate multiple node failures, the LRCs with \emph{$(r, \delta)$-locality} are further proposed. Since hot data is not uncommon in a distributed storage system, both Zeh \emph{et al.} and Kadhe \emph{et al.} focus on the LRCs with \emph{multiple localities or unequal localities} (ML-LRCs) recently, which said that the localities among the code symbols can be different. ML-LRCs are attractive and useful in reducing repair cost for hot data. In this paper, we generalize the ML-LRCs to the $(r,\delta)$-locality case of multiple node failures, and define an LRC with multiple $(r_{i}, \delta_{i})_{i\in [s]}$ localities ($s\ge 2$), where $r_{1}\leq r_{2}\leq\dots\leq r_{s}$ and $\delta_{1}\geq\delta_{2}\geq\dots\geq\delta_{s}\geq2$. Such codes ensure that some hot data could be repaired more quickly and have better failure-tolerance in certain cases because of relatively smaller $r_{i}$ and larger $\delta_{i}$. Then, we derive a Singleton-like upper bound on the minimum distance for the proposed LRCs by employing the regenerating-set technique. Finally, we obtain a class of explicit and structured constructions of optimal ML-LRCs, and further extend them to the cases of multiple $(r_{i}, \delta)_{i\in [s]}$ localities.

Includes members:
  Member "on the weight hierarchy of locally repairable codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "two classes of linear codes and their generalized hamming weights")
  Member "bounds and constructions of codes with multiple localities":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "codes with unequal locality":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "private information retrieval from locally repairable databases with colluding servers")
  Member "constructions and properties of linear locally repairable codes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "alphabet dependent bounds for linear locally repairable codes based on residual codes")
  Member "repair locality from a combinatorial perspective":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a tight rate bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures")
  Member "an integer programming based bound for locally repairable codes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "new bounds on the field size for maximally recoverable codes instantiating grid like topologies")
  Member "a family of optimal locally recoverable codes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "a locality based approach for coded computation")
  Member "optimal locally repairable linear codes":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "on optimal locally repairable codes and generalized sector disk 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.IT(Information Theory)