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 "grothendieck constant is norm of strassen matrix multiplication tensor"):
  Abstract: We show that two important quantities from two disparate areas of complexity theory --- Strassen's exponent of matrix multiplication $\omega$ and Grothendieck's constant $K_G$ --- are intimately related. They are different measures of size for the same underlying object --- the matrix multiplication tensor, i.e., the $3$-tensor or bilinear operator $\mu_{l,m,n} : \mathbb{F}^{l \times m} \times \mathbb{F}^{m \times n} \to \mathbb{F}^{l \times n}$, $(A,B) \mapsto AB$ defined by matrix-matrix product over $\mathbb{F} = \mathbb{R}$ or $\mathbb{C}$. It is well-known that Strassen's exponent of matrix multiplication is the greatest lower bound on (the log of) a tensor rank of $\mu_{l,m,n}$. We will show that Grothendieck's constant is the least upper bound on a tensor norm of $\mu_{l,m,n}$, taken over all $l, m, n \in \mathbb{N}$. Aside from relating the two celebrated quantities, this insight allows us to rewrite Grothendieck's inequality as a norm inequality \[ \lVert\mu_{l,m,n}\rVert_{1,2,\infty} =\max_{X,Y,M\neq0}\frac{|\operatorname{tr}(XMY)|}{\lVert X\rVert_{1,2}\lVert Y\rVert_{2,\infty}\lVert M\rVert_{\infty,1}}\leq K_G, \] and thereby allows a natural generalization to arbitrary $p,q, r$, $1\le p,q,r\le \infty$. We show that the following generalization is locally sharp: \[ \lVert\mu_{l,m,n}\rVert_{p,q,r}=\max_{X,Y,M\neq0}\frac{|\operatorname{tr}(XMY)|}{\|X\|_{p,q}\|Y\|_{q,r}\|M\|_{r,p}}\leq K_G \cdot l^{|1/q-1/2|} \cdot m^{1-1/p} \cdot n^{1/r}, \] and conjecture that Grothendieck's inequality is unique: $(p,q,r )=(1,2,\infty)$ is the only choice for which $\lVert\mu_{l,m,n}\rVert_{p,q,r}$ is uniformly bounded by a constant. We establish two-thirds of this conjecture: uniform boundedness of $\lVert\mu_{l,m,n}\rVert_{p,q,r}$ over all $l,m,n$ necessarily implies that $\min \{p,q,r\}=1$ and $\max \{p,q,r\}=\infty$.

Includes members:
  Member "powers of tensors and fast matrix multiplication":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")
  Member "nuclear norm of higher order tensors":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "multiresolution tensor learning for efficient and interpretable spatial analysis")
  Member "efficient algorithms for privately releasing marginals via convex relaxations":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the power of factorization mechanisms in local and central differential privacy")
  Member "grothendieck type inequalities in combinatorial optimization":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "adversarially robust low dimensional representations")
  Member "sharp kernel clustering algorithms and their associated grothendieck inequalities":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a sub constant improvement in approximating the positive semidefinite grothendieck problem")

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)