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 "inapproximability of the independent set polynomial in the complex plane"):
  Abstract: We study the complexity of approximating the independent set polynomial $Z_G(\lambda)$ of a graph $G$ with maximum degree $\Delta$ when the activity $\lambda$ is a complex number. #R##N#This problem is already well understood when $\lambda$ is real using connections to the $\Delta$-regular tree $T$. The key concept in that case is the "occupation ratio" of the tree $T$. This ratio is the contribution to $Z_T(\lambda)$ from independent sets containing the root of the tree, divided by $Z_T(\lambda)$ itself. If $\lambda$ is such that the occupation ratio converges to a limit, as the height of $T$ grows, then there is an FPTAS for approximating $Z_G(\lambda)$ on a graph $G$ with maximum degree $\Delta$. Otherwise, the approximation problem is NP-hard. #R##N#Unsurprisingly, the case where $\lambda$ is complex is more challenging. Peters and Regts identified the values of $\lambda$ for which the occupation ratio of the $\Delta$-regular tree converges. These values carve a cardioid-shaped region $\Lambda_\Delta$ in the complex plane. Motivated by the picture in the real case, they asked whether $\Lambda_\Delta$ marks the true approximability threshold for general complex values $\lambda$. #R##N#Our main result shows that for every $\lambda$ outside of $\Lambda_\Delta$, the problem of approximating $Z_G(\lambda)$ on graphs $G$ with maximum degree at most $\Delta$ is indeed NP-hard. In fact, when $\lambda$ is outside of $\Lambda_\Delta$ and is not a positive real number, we give the stronger result that approximating $Z_G(\lambda)$ is actually #P-hard. If $\lambda$ is a negative real number outside of $\Lambda_\Delta$, we show that it is #P-hard to even decide whether $Z_G(\lambda)>0$, resolving in the affirmative a conjecture of Harvey, Srivastava and Vondrak. #R##N#Our proof techniques are based around tools from complex analysis - specifically the study of iterative multivariate rational maps.

Includes members:
  Member "inapproximability of the independent set polynomial below the shearer threshold":
    also connected through other hyperedges:
      - Hyperedge HE-1 (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-2 (induced by source paper "commutative algorithms approximate the lll distribution")
  Member "computing the independence polynomial from the tree threshold down to the roots":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "the complexity of approximating complex valued ising and tutte partition functions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the complexity of approximating the matching polynomial in the complex plane")

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.CC(Computational Complexity)