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 the optimality of the kautz singleton construction in probabilistic group testing"):
  Abstract: We consider the probabilistic group testing problem where $d$ random defective items in a large population of $N$ items are identified with high probability by applying binary tests. It is known that $\Theta(d \log N)$ tests are necessary and sufficient to recover the defective set with vanishing probability of error when $d = O(N^{\alpha})$ for some $\alpha \in (0, 1)$. However, to the best of our knowledge, there is no explicit (deterministic) construction achieving $\Theta(d \log N)$ tests in general. In this work, we show that a famous construction introduced by Kautz and Singleton for the combinatorial group testing problem (which is known to be suboptimal for combinatorial group testing for moderate values of $d$) achieves the order optimal $\Theta(d \log N)$ tests in the probabilistic group testing problem when $d = \Omega(\log^2 N)$. This provides a strongly explicit construction achieving the order optimal result in the probabilistic group testing setting for a wide range of values of $d$. To prove the order-optimality of Kautz and Singleton's construction in the probabilistic setting, we provide a novel analysis of the probability of a non-defective item being covered by a random defective set directly, rather than arguing from combinatorial properties of the underlying code, which has been the main approach in the literature. Furthermore, we use a recursive technique to convert this construction into one that can also be efficiently decoded with only a log-log factor increase in the number of tests.

Includes members:
  Member "performance of group testing algorithms with near constant tests per item":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the all or nothing behavior of bernoulli group testing")
  Member "noisy non adaptive group testing a near definite defectives approach":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "learning erd h o s r enyi random graphs via edge detecting queries")
  Member "near optimal noisy group testing via separate decoding of items":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the all or nothing behavior of bernoulli group testing")
  Member "nearly optimal sparse group testing":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "group testing with runlength constraints for topological molecular storage")
  Member "nonadaptive group testing with random set of defectives":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "group testing an information theory perspective")
  Member "learning immune defectives graph through group tests":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "sparse combinatorial group testing for low energy massive random access")
  Member "saffron a fast efficient and robust framework for group testing based on sparse graph codes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on the all or nothing behavior of bernoulli group testing")
  Member "group testing algorithms bounds and simulations":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "serial quantization for sparse time sequences")

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)