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 "the algorithmic lll and the witness tree lemma"):
  Abstract: We consider the recent works of \cite{AIJACM,HV,Harmonic} that provide tools for analyzing focused stochastic local search algorithms that arise from algorithmizations of the Lovasz Local Lemma \cite{LLL} (LLL) in general probability spaces. These are algorithms which search a state space probabilistically by repeatedly selecting a "flaw" that is currently present and moving to a random nearby state in an effort to address it and, eventually, reach a flawless state. #R##N#While the original Moser-Tardos \cite{MT} (MT) algorithm is amenable to the analysis of these abstract frameworks, many follow-up results \cite{Haeupler_jacm,EnuHarris,szege_meet,determ,distributed,ParallelHarris} that further enhance, or exploit, our understanding of the MT process are not transferable to these general settings. Mainly, this is because a key ingredient of the original analysis of Moser and Tardos, the \emph{witness tree lemma}, does not longer hold. #R##N#In this work, we show that we can recover the witness tree lemma in the "commutative setting". The latter was recently introduced by Kolmogorov \cite{Kolmofocs} and captures the vast majority of the LLL applications. Armed with it, we focus on studying properties of commutative algorithms and give several applications. Among other things, we are able to generalize and extend to the commutative setting the main result of \cite{Haeupler_jacm} which states that the output of the MT algorithm well-approximates the conditional LLL-distribution, i.e., the distribution obtained by conditioning on all bad events being avoided.

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 "inapproximability of the independent set polynomial below the shearer threshold":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the complexity of approximating the matching polynomial in the complex plane")
  Member "computing the independence polynomial in shearer s region for the lll":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "commutative algorithms approximate the lll distribution")
  Member "algorithmic and enumerative aspects of the moser tardos distribution":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "deterministic algorithms for the lovasz local lemma simpler more general and more parallel")
  Member "parallel algorithms and concentration bounds for the lovasz local lemma via witness dags":
    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 "partial resampling to approximate covering integer programs":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on approximating partial set cover and generalizations")
  Member "an algorithmic proof of the lovasz local lemma via resampling oracles":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "extensions of the algorithmic lovasz local lemma")

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)