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 complexity of approximately counting tree homomorphisms"):
  Abstract: We study two computational problems, parameterised by a fixed tree H. #HOMSTO(H) is the problem of counting homomorphisms from an input graph G to H. #WHOMSTO(H) is the problem of counting weighted homomorphisms to H, given an input graph G and a weight function for each vertex v of G. Even though H is a tree, these problems turn out to be sufficiently rich to capture all of the known approximation behaviour in #P. We give a complete trichotomy for #WHOMSTO(H). If H is a star, then #WHOMSTO(H) is in FP. If H is not a star but it does not contain a certain induced subgraph J3, then #WHOMSTO(H) is equivalent under approximation-preserving (AP) reductions to #BIS, the problem of counting independent sets in a bipartite graph. This problem is complete for the class #RHΠ1 under AP-reductions. Finally, if H contains an induced J3, then #WHOMSTO(H) is equivalent under AP-reductions to #SAT, the problem of counting satisfying assignments to a CNF Boolean formula. Thus, #WHOMSTO(H) is complete for #P under AP-reductions. The results are similar for #HOMSTO(H) except that a rich structure emerges if H contains an induced J3. We show that there are trees H for which #HOMSTO(H) is #SAT-equivalent (disproving a plausible conjecture of Kelk). However, it is still not known whether #HOMSTO(H) is #SAT-hard for every tree H which contains an induced J3. It turns out that there is an interesting connection between these homomorphism-counting problems and the problem of approximating the partition function of the ferromagnetic Potts model. In particular, we show that for a family of graphs Jq, parameterised by a positive integer q, the problem #HOMSTO(Jq) is AP-interreducible with the problem of approximating the partition function of the q-state Potts model. It was not previously known that the Potts model had a homomorphism-counting interpretation. We use this connection to obtain some additional upper bounds for the approximation complexity of #HOMSTO(Jq).

Includes members:
  Member "the expressibility of functions on the boolean domain with applications to counting csps":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "lower bounds for testing graphical models colorings and antiferromagnetic ising models")
  Member "approximating the tutte polynomial of a binary matroid and other related combinatorial polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "log concave polynomials ii high dimensional walks and an fpras for counting bases of a matroid")
  Member "approximating the partition function of the ferromagnetic potts model":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "lower bounds for testing graphical models colorings and antiferromagnetic ising models")
  Member "an approximation trichotomy for boolean csp":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "lower bounds for testing graphical models colorings and antiferromagnetic ising models")

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)