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 "on maximally recoverable codes for product topologies"):
  Abstract: Given a topology of local parity-check constraints, a maximally recoverable code (MRC) can correct all erasure patterns that are information-theoretically correctable. In a grid-like topology, there are $a$ local constraints in every column forming a column code, $b$ local constraints in every row forming a row code, and $h$ global constraints in an $(m \times n)$ grid of codeword. Recently, Gopalan et al. initiated the study of MRCs under grid-like topology, and derived a necessary and sufficient condition, termed as the regularity condition, for an erasure pattern to be recoverable when $a=1, h=0$. #R##N#In this paper, we consider MRCs for product topology ($h=0$). First, we construct a certain bipartite graph based on the erasure pattern satisfying the regularity condition for product topology (any $a, b$, $h=0$) and show that there exists a complete matching in this graph. We then present an alternate direct proof of the sufficient condition when $a=1, h=0$. We later extend our technique to study the topology for $a=2, h=0$, and characterize a subset of recoverable erasure patterns in that case. For both $a=1, 2$, our method of proof is uniform, i.e., by constructing tensor product $G_{\text{col}} \otimes G_{\text{row}}$ of generator matrices of column and row codes such that certain square sub-matrices retain full rank. The full-rank condition is proved by resorting to the matching identified earlier and also another set of matchings in erasure sub-patterns.

Includes members:
  Member "maximally recoverable codes for grid like topologies":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "repair rate lower bounds for distributed storage")
  Member "new constructions of sd and mr codes over small finite fields":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "maximally recoverable codes with hierarchical locality")
  Member "explicit maximally recoverable codes with locality":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "on the locality of codeword symbols":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a locality based approach for coded computation")

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)