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 "a sharp threshold phenomenon for the distributed complexity of the lovasz local lemma"):
  Abstract: The Lovasz Local Lemma (LLL) says that, given a set of bad events that depend on the values of some random variables and where each event happens with probability at most $p$ and depends on at most $d$ other events, there is an assignment of the variables that avoids all bad events if the LLL criterion $ep(d+1)<1$ is satisfied. #R##N#In this paper, we study the dependency of the distributed complexity of the LLL problem on the chosen LLL criterion. We show that for the fundamental case of each random variable of the considered LLL instance being associated with an edge of the input graph, that is, each random variable influences at most two events, a sharp threshold phenomenon occurs at $p = 2^{-d}$: we provide a simple deterministic (!) algorithm that matches a known $\Omega(\log^* n)$ lower bound in bounded degree graphs, if $p < 2^{-d}$, whereas for $p \geq 2^{-d}$, a known $\Omega(\log \log n)$ randomized and a known $\Omega(\log n)$ deterministic lower bounds hold. #R##N#In many applications variables affect more than two events; our main contribution is to extend our algorithm to the case where random variables influence at most three different bad events. We show that, surprisingly, the sharp threshold occurs at the exact same spot, providing evidence for our conjecture that this phenomenon always occurs at $p = 2^{-d}$, independent of the number $r$ of events that are affected by a variable. Almost all steps of the proof framework we provide for the case $r=3$ extend directly to the case of arbitrary $r$; consequently, our approach serves as a step towards characterizing the complexity of the LLL under different exponential criteria.

Includes members:
  Member "on the complexity of distributed splitting problems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "deterministic coloring algorithms in the local model")
  Member "polylogarithmic time deterministic network decomposition and distributed derandomization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "massively parallel algorithms for distance approximation and spanners")
  Member "distributed approximation algorithms for maximum matching in graphs and hypergraphs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "distributed edge coloring in time quasi polylogarithmic in delta")
  Member "improved distributed degree splitting and edge coloring":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "distributed dense subgraph detection and low outdegree orientation")
  Member "a time hierarchy theorem for the local model":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "distributed graph problems through an automata theoretic lens")
  Member "on derandomizing local distributed algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "distributed maximum matching verification in congest")
  Member "distributed degree splitting edge coloring and orientations":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "distributed edge coloring in time quasi polylogarithmic in delta")
  Member "an exponential separation between randomized and deterministic complexity in the local model":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "truly tight in delta bounds for bipartite maximal matching and variants")

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.DS(Data Structures and Algorithms)