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 "tight lower bounds on the number of faces of the minkowski sum of convex polytopes via the cayley trick"):
  Abstract: Consider a set of $r$ convex $d$-polytopes $P_1,P_2,...,P_r$, where $d\ge{}3$ and $r\ge{}2$, and let $n_i$ be the number of vertices of $P_i$, $1\le{}i\le{}r$. It has been shown by Fukuda and Weibel that the number of $k$-faces of the Minkowski sum, $P_1+P_2+...+P_r$, is bounded from above by $\Phi_{k+r}(n_1,n_2,...,n_r)$, where $\Phi_{\ell}(n_1,n_2,...,n_r)= \sum_{\substack{1\le{}s_i\le{}n_i s_1+...+s_r=\ell}} \prod_{i=1}^r\binom{n_i}{s_i}$, $\ell\ge{}r$. Fukuda and Weibel have also shown that the upper bound mentioned above is tight for $d\ge{}4$, $2\le{}r\le{}\lfloor\frac{d}{2}\rfloor$, and for all $0\le{}k\le{}\lfloor\frac{d}{2}\rfloor-r$. #R##N#In this paper we construct a set of $r$ neighborly $d$-polytopes $P_1,P_2,...,P_r$, where $d\ge{}3$ and $2\le{}r\le{}d-1$, for which the upper bound of Fukuda and Weibel is attained for all $0\le{}k\le{}\lfloor\frac{d+r-1}{2}\rfloor-r$. Our approach is based on what is known as the Cayley trick for Minkowski sums. A direct consequence of our result is a tight asymptotic bound on the complexity of the Minkowski sum $P_1+P_2+...+P_r$, for any fixed dimension $d$ and any $2\le{}r\le{}d-1$, when the number of vertices of the polytopes is (asymptotically) the same.

Includes members:
  Member "the maximum number of faces of the minkowski sum of two convex polytopes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "log concavity and lower bounds for arithmetic circuits")
  Member "convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the maximum number of faces of the minkowski sum of two convex polytopes")
  Member "minkowski sum construction and other applications of arrangements of geodesic arcs on the sphere":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the maximum number of faces of the minkowski sum of two convex polytopes")

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.CG(Computational Geometry)