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: "approximability and proof complexity"
  Abstract: This work is concerned with the proof-complexity of certifying that optimization problems do \emph{not} have good solutions. Specifically we consider bounded-degree "Sum of Squares" (SOS) proofs, a powerful algebraic proof system introduced in 1999 by Grigoriev and Vorobjov. Work of Shor, Lasserre, and Parrilo shows that this proof system is automatizable using semidefinite programming (SDP), meaning that any $n$-variable degree-$d$ proof can be found in time $n^{O(d)}$. Furthermore, the SDP is dual to the well-known Lasserre SDP hierarchy, meaning that the "$d/2$-round Lasserre value" of an optimization problem is equal to the best bound provable using a degree-$d$ SOS proof. These ideas were exploited in a recent paper by Barak et al.\ (STOC 2012) which shows that the known "hard instances" for the Unique-Games problem are in fact solved close to optimally by a constant level of the Lasserre SDP hierarchy. #R##N#We continue the study of the power of SOS proofs in the context of difficult optimization problems. In particular, we show that the Balanced-Separator integrality gap instances proposed by Devanur et al.\ can have their optimal value certified by a degree-4 SOS proof. The key ingredient is an SOS proof of the KKL Theorem. We also investigate the extent to which the Khot--Vishnoi Max-Cut integrality gap instances can have their optimum value certified by an SOS proof. We show they can be certified to within a factor .952 ($> .878$) using a constant-degree proof. These investigations also raise an interesting mathematical question: is there a constant-degree SOS proof of the Central Limit Theorem?

Connected through hyperedge HE-1 (induced by source paper "efficiently learning structured distributions from untrusted batches"):
  with members:
    - "list decodable linear regression"
    - "list decodable learning via sum of squares"
    - "high dimensional estimation via sum of squares proofs"
    - "federated learning strategies for improving communication efficiency"
    - "being robust in high dimensions can be practical"
    - "list decodable robust mean estimation and learning mixtures of spherical gaussians"
    - "learning discrete distributions from untrusted batches"
    - "learning populations of parameters"

Connected through hyperedge HE-2 (induced by source paper "sum of squares meets square loss fast rates for agnostic tensor completion"):
  with members:
    - "efficient algorithms for outlier robust regression"
    - "exact tensor completion with sum of squares"
    - "sum of squares lower bounds for refuting any csp"
    - "spectral algorithms for tensor completion"
    - "strongly refuting random csps below the spectral threshold"
    - "complexity theoretic limitations on learning halfspaces"
    - "learning without concentration"
    - "nuclear norm of higher order tensors"

Connected through hyperedge HE-3 (induced by source paper "semi algebraic proofs ips lower bounds and the tau conjecture can a natural number be negative"):
  with members:
    - "proof complexity lower bounds from algebraic circuit complexity"
    - "algebraic proof complexity progress frontiers and challenges"
    - "characterizing propositional proofs as non commutative formulas"
    - "communication lower bounds via critical block sensitivity"
    - "hypercontractivity sum of squares proofs and their applications"

Connected through hyperedge HE-4 (induced by source paper "sum of squares meets nash optimal lower bounds for finding any equilibrium"):
  with members:
    - "better agnostic clustering via relaxed tensor norms"
    - "sum of squares lower bounds for refuting any csp"
    - "strongly refuting random csps below the spectral threshold"
    - "how to refute a random csp"
    - "hypercontractivity sum of squares proofs and their applications"
    - "settling the complexity of computing two player nash equilibria"
    - "games of fixed rank a hierarchy of bimatrix games"

Connected through hyperedge HE-5 (induced by source paper "mildly exponential time approximation algorithms for vertex cover uniform sparsest cut and related problems"):
  with members:
    - "sum of squares lower bounds for refuting any csp"
    - "sum of squares proofs and the quest toward optimal algorithms"
    - "hypercontractivity sum of squares proofs and their applications"
    - "reductions between expansion problems"

Connected through hyperedge HE-6 (induced by source paper "mixture models robustness and sum of squares proofs"):
  with members:
    - "thresholding based efficient outlier robust pca"
    - "learning geometric concepts with nasty noise"
    - "outlier robust moment estimation via sum of squares"
    - "being robust in high dimensions can be practical"
    - "on the bit complexity of sum of squares proofs"
    - "exact tensor completion with sum of squares"
    - "better agnostic clustering via relaxed tensor norms"
    - "robustly learning a gaussian getting optimal error efficiently"

Connected through hyperedge HE-7 (induced by source paper "sum of squares lower bounds for refuting any csp"):
  with members:
    - "lower bounds for csp refutation by sdp hierarchies"
    - "the backtracking survey propagation algorithm for solving random k sat problems"
    - "strongly refuting random csps below the spectral threshold"
    - "how to refute a random csp"
    - "noisy tensor completion via the sum of squares hierarchy"
    - "complexity theoretic limitations on learning halfspaces"
    - "sum of squares lower bounds from pairwise independence"
    - "lower bounds on the size of semidefinite programming relaxations"

Connected through hyperedge HE-8 (induced by source paper "the limits of sdp relaxations for general valued csps"):
  with members:
    - "the power of sherali adams relaxations for general valued csps"
    - "the complexity of finite valued csps"
    - "approximating rectangles by juntas and weakly exponential lower bounds for lp relaxations of csps"
    - "from weak to strong lp gaps for all csps"
    - "algebraic properties of valued constraint satisfaction problem"
    - "the complexity of general valued csps"
    - "robustly solvable constraint satisfaction problems"
    - "lower bounds on the size of semidefinite programming relaxations"

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.CC(Computational Complexity)