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 "imperfect gaps in gap eth and pcps"):
  Abstract: We study the role of perfect completeness in probabilistically checkable proof systems (PCPs) and give a new way to transform a PCP with imperfect completeness to a PCP with perfect completeness when the initial gap is a constant. In particular, we show that $\text{PCP}_{c,s}[r,q] \subseteq \text{PCP}_{1,1-\Omega(1)}[r+O(1),q+O(r)]$, for $c-s=\Omega(1)$. This implies that one can convert imperfect completeness to perfect in linear-sized PCPs for $NTIME[O(n)]$ with a $O(\log n)$ additive loss in the query complexity $q$. We show our result by constructing a "robust circuit" using threshold gates. These results are a gap amplification procedure for PCPs (when completeness is imperfect), analogous to questions studied in parallel repetition and pseudorandomness. #R##N#We also investigate the time complexity of approximating perfectly satisfiable instances of 3SAT versus those with imperfect completeness. We show that the Gap-ETH conjecture without perfect completeness is equivalent to Gap-ETH with perfect completeness, i.e. we show that Gap-3SAT, where the gap is not around 1, has a subexponential algorithm, if and only if, Gap-3SAT with perfect completeness has subexponential algorithms. We also relate the time complexities of these two problems in a more fine-grained way, to show that $T_2(n) \leq T_1(n(\log\log n)^{O(1)})$, where $T_1(n),T_2(n)$ denote the randomized time-complexity of approximating MAX 3SAT with perfect and imperfect completeness, respectively.

Includes members:
  Member "gap s eth hardness of svp":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "hardness of bounded distance decoding on lattices in ell_p norms")
  Member "from gap eth to fpt inapproximability clique dominating set and more":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "parameterized inapproximability for steiner orientation by gap amplification")
  Member "a birthday repetition theorem and complexity of approximating dense csps":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "parameterized inapproximability for steiner orientation by gap amplification")

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)