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 "locality of not so weak coloring"):
  Abstract: Many graph problems are locally checkable: a solution is globally feasible if it looks valid in all constant-radius neighborhoods. This idea is formalized in the concept of locally checkable labelings (LCLs), introduced by Naor and Stockmeyer (1995). Recently, Chang et al. (2016) showed that in bounded-degree graphs, every LCL problem belongs to one of the following classes: #R##N#- "Easy": solvable in $O(\log^* n)$ rounds with both deterministic and randomized distributed algorithms. #R##N#- "Hard": requires at least $\Omega(\log n)$ rounds with deterministic and $\Omega(\log \log n)$ rounds with randomized distributed algorithms. #R##N#Hence for any parameterized LCL problem, when we move from local problems towards global problems, there is some point at which complexity suddenly jumps from easy to hard. For example, for vertex coloring in $d$-regular graphs it is now known that this jump is at precisely $d$ colors: coloring with $d+1$ colors is easy, while coloring with $d$ colors is hard. #R##N#However, it is currently poorly understood where this jump takes place when one looks at defective colorings. To study this question, we define $k$-partial $c$-coloring as follows: nodes are labeled with numbers between $1$ and $c$, and every node is incident to at least $k$ properly colored edges. #R##N#It is known that $1$-partial $2$-coloring (a.k.a. weak $2$-coloring) is easy for any $d \ge 1$. As our main result, we show that $k$-partial $2$-coloring becomes hard as soon as $k \ge 2$, no matter how large a $d$ we have. #R##N#We also show that this is fundamentally different from $k$-partial $3$-coloring: no matter which $k \ge 3$ we choose, the problem is always hard for $d = k$ but it becomes easy when $d \gg k$. The same was known previously for partial $c$-coloring with $c \ge 4$, but the case of $c < 4$ was open.

Includes members:
  Member "distributed recoloring":
    also connected through other hyperedges:
      (none)
  Member "almost global problems in the local model":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "distributed graph problems through an automata theoretic lens")
  Member "improved distributed delta coloring":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "faster deterministic distributed coloring through recursive list coloring")
  Member "the complexity of distributed edge coloring with small palettes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "distributed edge coloring in time quasi polylogarithmic in delta")
  Member "sublogarithmic distributed algorithms for lov asz local lemma and the complexity hierarchy":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "classification of distributed binary labeling problems")
  Member "new classes of distributed time complexity":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "distributed graph problems through an automata theoretic lens")
  Member "a time hierarchy theorem for the local model":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "distributed graph problems through an automata theoretic lens")
  Member "lcl problems on grids":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "an automatic speedup theorem for distributed problems")

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.DC(Distributed, Parallel, and Cluster Computing)