human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "the propagation depth of local consistency"
  Abstract: We establish optimal bounds on the number of nested propagation steps in $k$-consistency tests. It is known that local consistency algorithms such as arc-, path- and $k$-consistency are not efficiently parallelizable. Their inherent sequential nature is caused by long chains of nested propagation steps, which cannot be executed in parallel. This motivates the question "What is the minimum number of nested propagation steps that have to be performed by $k$-consistency algorithms on (binary) constraint networks with $n$ variables and domain size $d$?" #R##N#It was known before that 2-consistency requires $\Omega(nd)$ and 3-consistency requires $\Omega(n^2)$ sequential propagation steps. We answer the question exhaustively for every $k\geq 2$: there are binary constraint networks where any $k$-consistency procedure has to perform $\Omega(n^{k-1}d^{k-1})$ nested propagation steps before local inconsistencies were detected. This bound is tight, because the overall number of propagation steps performed by $k$-consistency is at most $n^{k-1}d^{k-1}$.

Connected through hyperedge HE-1 (induced by source paper "walk refinement walk logic and the iteration number of the weisfeiler leman algorithm"):
  with members:
    - "linear diophantine equations group csps and graph isomorphism"
    - "near optimal lower bounds on quantifier depth and weisfeiler leman refinement steps"
    - "upper bounds on the quantifier depth for graph differentiation in first order logic"

Connected through hyperedge HE-2 (induced by source paper "upper bounds on the quantifier depth for graph differentiation in first order logic"):
  with members:
    - "near optimal lower bounds on quantifier depth and weisfeiler leman refinement steps"
    - "graph isomorphism in quasipolynomial time"
    - "graphs identified by logics with counting"
    - "tight lower and upper bounds for the complexity of canonical colour refinement"
    - "universal covers color refinement and two variable counting logic lower bounds for the depth"
    - "practical graph isomorphism ii"
    - "dimension reduction via colour refinement"
    - "from invariants to canonization in parallel"

Connected through hyperedge HE-3 (induced by source paper "near optimal lower bounds on quantifier depth and weisfeiler leman refinement steps"):
  with members:
    - "upper bounds on the quantifier depth for graph differentiation in first order logic"
    - "graph isomorphism in quasipolynomial time"
    - "a generalized method for proving polynomial calculus degree lower bounds"
    - "universal covers color refinement and two variable counting logic lower bounds for the depth"
    - "pebble games proof complexity and time space trade offs"
    - "understanding space in proof complexity separations and trade offs via substitutions"

Connected through hyperedge HE-4 (induced by source paper "on the speed of constraint propagation and the time complexity of arc consistency testing"):
  with members:
    - "lower bounds for existential pebble games and k consistency tests"
    - "graph logics with rational relations"
    - "bounds for the quantifier depth in finite variable logics alternation hierarchy"
    - "on the complexity of finding narrow proofs"

Question: Please tell me which class the center node 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.AI(Artificial Intelligence)