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 "on the complexity of restoring corrupted colorings"):
  Abstract: In the \probrFix problem, we are given a graph $G$, a (non-proper) vertex-coloring $c : V(G) \to [r]$, and a positive integer $k$. The goal is to decide whether a proper $r$-coloring $c'$ is obtainable from $c$ by recoloring at most $k$ vertices of $G$. Recently, Junosza-Szaniawski, Liedloff, and Rz{\k{a}}{\.z}ewski [SOFSEM 2015] asked whether the problem has a polynomial kernel parameterized by the number of recolorings $k$. In a full version of the manuscript, the authors together with Garnero and Montealegre, answered the question in the negative: for every $r \geq 3$, the problem \probrFix does not admit a polynomial kernel unless $\NP \subseteq \coNP / \poly$. Independently of their work, we give an alternative proof of the theorem. Furthermore, we study the complexity of \probrFixSwap, where the only difference from \probrFix is that instead of $k$ recolorings we have a budget of $k$ color swaps. We show that for every $r \geq 3$, the problem \probrFixSwap is $\W[1]$-hard whereas \probrFix is known to be FPT. Moreover, when $r$ is part of the input, we observe both \probFix and \probFixSwap are $\W[1]$-hard parameterized by treewidth. We also study promise variants of the problems, where we are guaranteed that a proper $r$-coloring $c'$ is indeed obtainable from $c$ by some finite number of swaps. For instance, we prove that for $r=3$, the problems \probrFixPromise and \probrFixSwapPromise are $\NP$-hard for planar graphs. As a consequence of our reduction, the problems cannot be solved in $2^{o(\sqrt{n})}$ time unless the Exponential Time Hypothesis (ETH) fails.

Includes members:
  Member "on the hardness of losing weight":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "kernelization of constraint satisfaction problems a study through universal algebra")
  Member "fine grained complexity analysis of two classic tsp variants":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "maintaining the union of unit discs under insertions with near optimal overhead")
  Member "fixing improper colorings of graphs":
    also connected through other hyperedges:
      (none)
  Member "finding shortest paths between graph colourings":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "shortest reconfiguration of perfect matchings via alternating cycles")
  Member "reconfiguration in bounded bandwidth and treedepth":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "independent set reconfiguration thresholds of hereditary graph classes")
  Member "kernelization lower bounds by cross composition":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "subexponential parameterized algorithms and kernelization on almost chordal graphs")
  Member "adaptive uncertainty resolution in bayesian combinatorial optimization problems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the markovian price of information")

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)