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 power of linear programming for general valued csps"
  Abstract: Let $D$, called the domain, be a fixed finite set and let $\Gamma$, called the valued constraint language, be a fixed set of functions of the form $f:D^m\to\mathbb{Q}\cup\{\infty\}$, where different functions might have different arity $m$. We study the valued constraint satisfaction problem parametrised by $\Gamma$, denoted by VCSP$(\Gamma)$. These are minimisation problems given by $n$ variables and the objective function given by a sum of functions from $\Gamma$, each depending on a subset of the $n$ variables. Finite-valued constraint languages contain functions that take on only rational values and not infinite values. #R##N#Our main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation (BLP). For a valued constraint language $\Gamma$, BLP is a decision procedure for $\Gamma$ if and only if $\Gamma$ admits a symmetric fractional polymorphism of every arity. For a finite-valued constraint language $\Gamma$, BLP is a decision procedure if and only if $\Gamma$ admits a symmetric fractional polymorphism of some arity, or equivalently, if $\Gamma$ admits a symmetric fractional polymorphism of arity 2. #R##N#Using these results, we obtain tractability of several novel classes of problems, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) $k$-submodular on arbitrary finite domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees.

Connected through hyperedge HE-1 (induced by source paper "graphical models and belief propagation hierarchy for physics constrained network flows"):
  with members:
    - "how to calculate partition functions using convex programming hierarchies provable bounds for variational methods"
    - "minimum weight perfect matching via blossom belief propagation"
    - "a differential analysis of the power flow equations"
    - "solving the power flow equations a monotone operator approach"
    - "submodular functions from discrete to continous domains"
    - "natural gas flow solutions with guarantees a monotone operator theory approach"
    - "optimal compression in natural gas networks a geometric programming approach"
    - "tightening lp relaxations for map using message passing"

Connected through hyperedge HE-2 (induced by source paper "on planar valued csps"):
  with members:
    - "the power of sherali adams relaxations for general valued csps"
    - "even delta matroids and the complexity of planar boolean csps"
    - "the complexity of finite valued csps"
    - "a galois connection for weighted relational clones of infinite size"
    - "necessary conditions for tractability of valued csps"
    - "hybrid v csps and algebraic reductions"
    - "algebraic properties of valued constraint satisfaction problem"
    - "the complexity of general valued csps"

Connected through hyperedge HE-3 (induced by source paper "the complexity of finite valued csps"):
  with members:
    - "an algebraic theory of complexity for discrete optimization"
    - "the complexity of conservative valued csps"
    - "computational complexity of the minimum cost homomorphism problem on three element domains"
    - "tractable triangles and cross free convexity in discrete optimisation"
    - "the power of linear programming for valued csps"
    - "an effective fusion technique of cloud computing and networking series"
    - "tractable optimization problems through hypergraph based structural restrictions"
    - "the power of linear programming for valued csps a constructive characterization"

Connected through hyperedge HE-4 (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"

Connected through hyperedge HE-5 (induced by source paper "a galois connection for weighted relational clones of infinite size"):
  with members:
    - "the power of sherali adams relaxations for general valued csps"
    - "the complexity of finite valued csps"
    - "necessary conditions for tractability of valued csps"
    - "algebraic properties of valued constraint satisfaction problem"
    - "the complexity of general valued csps"
    - "sherali adams relaxations for valued csps"
    - "an algebraic theory of complexity for discrete optimization"
    - "the complexity of conservative valued csps"

Connected through hyperedge HE-6 (induced by source paper "the complexity of general valued csps"):
  with members:
    - "the power of sherali adams relaxations for general valued csps"
    - "combinatorial optimization algorithms via polymorphisms"
    - "a galois connection for valued constraint languages of infinite size"
    - "algebraic properties of valued constraint satisfaction problem"
    - "effectiveness of structural restrictions for hybrid csps"
    - "local distribution and the symmetry gap approximability of multiway partitioning problems"
    - "sherali adams relaxations for valued csps"
    - "robustly solvable constraint satisfaction problems"

Connected through hyperedge HE-7 (induced by source paper "edge bipartization faster than 2 k"):
  with members:
    - "on problems as hard as cnf sat"
    - "parameterized algorithms on perfect graphs for deletion to r ell graphs"
    - "an o 1 84 k parameterized algorithm for the multiterminal cut problem"
    - "half integrality lp branching and fpt algorithms"
    - "faster parameterized algorithms using linear programming"
    - "fast hamiltonicity checking via bases of perfect matchings"
    - "solving connectivity problems parameterized by treewidth in single exponential time"
    - "compression via matroids a randomized polynomial kernel for odd cycle transversal"

Connected through hyperedge HE-8 (induced by source paper "necessary conditions for tractability of valued csps"):
  with members:
    - "algebraic properties of valued constraint satisfaction problem"
    - "a reduction from valued csp to min cost homomorphism problem for digraphs"
    - "the complexity of general valued csps"
    - "computational complexity of the minimum cost homomorphism problem on three element domains"
    - "an effective fusion technique of cloud computing and networking series"
    - "the power of linear programming for valued csps a constructive characterization"
    - "extensions of the minimum cost homomorphism problem"

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)