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 "parameterized inapproximability for steiner orientation by gap amplification"):
  Abstract: In the $k$-Steiner Orientation problem, we are given a mixed graph, that is, with both directed and undirected edges, and a set of $k$ terminal pairs. The goal is to find an orientation of the undirected edges that maximizes the number of terminal pairs for which there is a path from the source to the sink. The problem is known to be W[1]-hard when parameterized by k and hard to approximate up to some constant for FPT algorithms assuming Gap-ETH. On the other hand, no approximation factor better than $O(k)$ is known.  We show that $k$-Steiner Orientation is unlikely to admit an approximation algorithm with any constant factor, even within FPT running time. To obtain this result, we construct a self-reduction via a hashing-based gap amplification technique, which turns out useful even outside of the FPT paradigm. Precisely, we rule out any approximation factor of the form $(\log k)^{o(1)}$ for FPT algorithms (assuming FPT $\ne$ W[1]) and $(\log n)^{o(1)}$ for~purely polynomial-time algorithms (assuming that the class W[1] does not admit randomized FPT algorithms). Moreover, we prove $k$-Steiner Orientation to belong to W[1], which entails W[1]-completeness of $(\log k)^{o(1)}$-approximation for $k$-Steiner Orientation This provides an example of a natural approximation task that is complete in a parameterized complexity class.  Finally, we apply our technique to the maximization version of directed multicut - Max $(k,p)$-Directed Multicut - where we are given a directed graph, $k$ terminals pairs, and a budget $p$. The goal is to maximize the number of separated terminal pairs by removing $p$ edges. We present a simple proof that the problem admits no FPT approximation with factor $O(k^{\frac 1 2 - \epsilon})$ (assuming FPT $\ne$ W[1]) and no polynomial-time approximation with ratio $O(|E(G)|^{\frac 1 2 - \epsilon})$ (assuming NP $\not\subseteq$ co-RP).

Includes members:
  Member "tight fpt approximations for k median and k means":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "fair algorithms for clustering")
  Member "constant factor fpt approximation for capacitated k median":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "fair clustering with multiple colors")
  Member "faster exact and approximate algorithms for k cut":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the number of minimum k cuts improving the karger stein bound")
  Member "from gap eth to fpt inapproximability clique dominating set and more":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "approximating subset sum is equivalent to min plus convolution")
  Member "completely inapproximable monotone and antimonotone parameterized problems":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "inapproximability within w 1 the case of steiner orientation")
  Member "almost polynomial ratio eth hardness of approximating densest k subgraph":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "optimizing item and subgroup configurations for social aware vr shopping")
  Member "a birthday repetition theorem and complexity of approximating dense csps":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "tight running time lower bounds for strong inapproximability of maximum k coverage unique set cover and related problems via t wise agreement testing theorem")
  Member "directed multicut is w 1 hard even for four terminal pairs":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "tight bounds for planar strongly connected steiner subgraph with fixed number of terminals and extensions")

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)