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 "parameterizing the permanent genus apices minors evaluation mod 2 k"):
  Abstract: We identify and study relevant structural parameters for the problem PerfMatch of counting perfect matchings in a given input graph $G$. These generalize the well-known tractable planar case, and they include the genus of $G$, its apex number (the minimum number of vertices whose removal renders $G$ planar), and its Hadwiger number (the size of a largest clique minor). #R##N#To study these parameters, we first introduce the notion of combined matchgates, a general technique that bridges parameterized counting problems and the theory of so-called Holants and matchgates: Using combined matchgates, we can simulate certain non-existing gadgets $F$ as linear combinations of $t=O(1)$ existing gadgets. If a graph $G$ features $k$ occurrences of $F$, we can then reduce $G$ to $t^k$ graphs that feature only existing gadgets, thus enabling parameterized reductions. #R##N#As applications of this technique, we simplify known $4^g n^{O(1)}$ time algorithms for PerfMatch on graphs of genus $g$. Orthogonally to this, we show #W[1]-hardness of the permanent on $k$-apex graphs, implying its #W[1]-hardness under the Hadwiger number. Additionally, we rule out $n^{o(k/\log k)}$ time algorithms under the counting exponential-time hypothesis #ETH. #R##N#Finally, we use combined matchgates to prove parity-W[1]-hardness of evaluating the permanent modulo $2^k$, complementing an $O(n^{4k-3})$ time algorithm by Valiant and answering an open question of Bj\"orklund. We also obtain a lower bound of $n^{\Omega(k/\log k)}$ under the parity version of the exponential-time hypothesis.

Includes members:
  Member "exponential time complexity of the permanent and the tutte polynomial":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the fine grained complexity of computing the tutte polynomial of a linear matroid")
  Member "complexity of counting subgraphs only the boundedness of the vertex cover number counts":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "tight bounds for planar strongly connected steiner subgraph with fixed number of terminals and extensions")
  Member "counting perfect matchings in graphs that exclude a single crossing minor":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a new family of tractable ising models")
  Member "everything you always wanted to know about the parameterized complexity of subgraph isomorphism but were afraid to ask":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "almost tight lower bounds for hard cutting problems in embedded graphs")
  Member "obtaining a planar graph by vertex deletion":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "hitting topological minor models in planar graphs is fixed parameter tractable")

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)