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 within w 1 the case of steiner orientation"):
  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 better than $O(k)$ is known. #R##N#We show that $k$-Steiner Orientation admits no sublogarithmic approximation algorithm, even with a parameterized running time, assuming W[1] $\ne$ FPT. To obtain this result, we reduce the problem to itself via a hashing-based gap amplification technique, which turns out useful even outside of the FPT paradigm. Precisely, we rule out any approximation ratio of the form $(\log k)^{o(1)}$ for parameterized algorithms and $(\log n)^{o(1)}$ for purely polynomial running time, under the same assumption. This constitutes a novel inapproximability result for polynomial time algorithms obtained via tools from the FPT theory. Moreover, we prove $k$-Steiner Orientation to be W[1]-complete, what provides an example of a natural approximation task that is complete in a parameterized complexity class. #R##N#Finally, we apply our technique to the maximization version of Directed Multicut and obtain a simple proof that the problem admits no FPT approximation with ratio $O(k^{\frac 1 2 - \epsilon})$ (assuming W[1] $\ne$ FPT) and no polynomial-time approximation with ratio $O(m^{\frac 1 2 - \epsilon})$ (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 "parameterized inapproximability for steiner orientation by gap amplification")
  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 "parameterized inapproximability for steiner orientation by gap amplification")
  Member "from gap eth to fpt inapproximability clique dominating set and more":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "parameterized inapproximability for steiner orientation by gap amplification")
  Member "completely inapproximable monotone and antimonotone parameterized problems":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "parameterized inapproximability for steiner orientation by gap amplification")
  Member "directed multicut is w 1 hard even for four terminal pairs":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "parameterized inapproximability for steiner orientation by gap amplification")
  Member "the parameterized complexity of k biclique":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "parameterized inapproximability for steiner orientation by gap amplification")
  Member "steiner forest orientation problems":
    also connected through other hyperedges:
      - Hyperedge HE-8 (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)