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 "variable version lov asz local lemma beyond shearer s bound"):
  Abstract: A tight criterion under which the abstract version Lov\'asz Local Lemma (abstract-LLL) holds was given by Shearer decades ago. However, little is known about that of the variable version LLL (variable-LLL) where events are generated by independent random variables, though this model of events is applicable to almost all applications of LLL. We introduce a necessary and sufficient criterion for variable-LLL, in terms of the probabilities of the events and the event-variable graph specifying the dependency among the events. Based on this new criterion, we obtain boundaries for two families of event-variable graphs, namely, cyclic and treelike bigraphs. These are the first two non-trivial cases where the variable-LLL boundary is fully determined. As a byproduct, we also provide a universal constructive method to find a set of events whose union has the maximum probability, given the probability vector and the event-variable graph. Though it is #P-hard in general to determine variable-LLL boundaries, we can to some extent decide whether a gap exists between a variable-LLL boundary and the corresponding abstract-LLL boundary. In particular, we show that the gap existence can be decided without solving Shearer's conditions or checking our variable-LLL criterion. Equipped with this powerful theorem, we show that there is no gap if the base graph of the event-variable graph is a tree, while gap appears if the base graph has an induced cycle of length at least 4. The problem is almost completely solved except when the base graph has only 3-cliques, in which case we also get partial solutions. A set of reduction rules are established that facilitate to infer gap existence of an event-variable graph from known ones. As an application, various event-variable graphs, in particular combinatorial ones, are shown to be gapful/gapless.

Includes members:
  Member "lopsidependency in the moser tardos framework beyond the lopsided lovasz local lemma":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "deterministic algorithms for the lovasz local lemma simpler more general and more parallel")
  Member "deterministic parallel algorithms for fooling polylogarithmic juntas and the lovasz local lemma":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "deterministic algorithms for the lovasz local lemma simpler more general and more parallel")
  Member "uniform sampling through the lov asz local lemma":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "dynamic mcmc sampling")
  Member "computing the independence polynomial in shearer s region for the lll":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "commutative algorithms approximate the lll distribution")
  Member "approximate counting the lovasz local lemma and inference in graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "fast sampling and counting k sat solutions in the local lemma regime")
  Member "focused stochastic local search and the lov asz local lemma":
    also connected through other hyperedges:
      (none)
  Member "commutativity in the algorithmic lovasz local lemma":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "extensions of the algorithmic lovasz local lemma")
  Member "parallel algorithms and concentration bounds for the lovasz local lemma via witness dags":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "fast sampling and counting k sat solutions in the local lemma regime")

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.DM(Discrete Mathematics)