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 "lower bounds on the size of semidefinite programming relaxations"):
  Abstract: We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the linear image of the feasible region of any SDP (i.e., any spectrahedron) of dimension less than $2^{n^c}$, for some constant $c > 0$. This result yields the first super-polynomial lower bounds on the semidefinite extension complexity of any explicit family of polytopes. #R##N#Our results follow from a general technique for proving lower bounds on the positive semidefinite rank of a matrix. To this end, we establish a close connection between arbitrary SDPs and those arising from the sum-of-squares SDP hierarchy. For approximating maximum constraint satisfaction problems, we prove that SDPs of polynomial-size are equivalent in power to those arising from degree-$O(1)$ sum-of-squares relaxations. This result implies, for instance, that no family of polynomial-size SDP relaxations can achieve better than a 7/8-approximation for MAX-3-SAT.

Includes members:
  Member "analysis of boolean functions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "sum of squares proofs and the quest toward optimal algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "sum of squares bounds for the ordering principle")
  Member "rounding sum of squares relaxations":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "approximate constraint satisfaction requires large lp relaxations":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "new dependencies of hierarchies in polynomial optimization")
  Member "on the existence of 0 1 polytopes with high semidefinite extension complexity":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on modeling hard combinatorial optimization problems as linear programs refutations of the unconditional impossibility claims")
  Member "the matching polytope has exponential extension complexity":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "extended formulation lower bounds for refuting random csps")
  Member "approximation limits of linear programs beyond hierarchies":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "compressing permutation groups into grammars and polytopes a graph embedding approach")
  Member "hypercontractivity sum of squares proofs and their applications":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "sum of squares bounds for the ordering principle")

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.CC(Computational Complexity)