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 "reliability of erasure coded storage systems a combinatorial geometric approach"):
  Abstract: We consider the probability of data loss, or equivalently, the reliability function for an erasure coded distributed data storage system under worst case conditions. Data loss in an erasure coded system depends on probability distributions for the disk repair duration and the disk failure duration. In previous works, the data loss probability of such systems has been studied under the assumption of exponentially distributed disk failure and disk repair durations, using well-known analytic methods from the theory of Markov processes. These methods lead to an estimate of the integral of the reliability function. Here, we address the problem of directly calculating the data loss probability for general repair and failure duration distributions. A closed limiting form is developed for the probability of data loss, and it is shown that the probability of the event that a repair duration exceeds a failure duration is sufficient for characterizing the data loss probability. For the case of constant repair duration, we develop an expression for the conditional data loss probability given the number of failures experienced by a each node in a given time window. We do so by developing a geometric approach that relies on the computation of volumes of a family of polytopes that are related to the code. An exact calculation is provided, and an upper bound on the data loss probability is obtained by posing the problem as a set avoidance problem. Theoretical calculations are compared with simulation results.

Includes members:
  Member "reliability models for highly fault tolerant storage systems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "distributed data storage systems with opportunistic repair")
  Member "high rate regenerating codes through layering":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a connection between locally repairable codes and exact regenerating 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.DC(Distributed, Parallel, and Cluster Computing)