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 "small lifts of expander graphs are expanding"):
  Abstract: A k-lift of an n-vertex base-graph G is a graph H on $n \times k$ vertices, where each vertex of G is replaced by k vertices and each edge (u,v) in G is replaced by a matching representing a bijection $\pi_{uv}$ so that the edges of H are of the form $\big ((u,i),(v,\pi_{uv}(i))\big )$. H s a (uniformly) random lift of G if for every edge (u,v) the bijection $\pi_{uv}$ is chosen uniformly and independently at random. The main motivation for studying lifts has been understanding Ramanujan expander graphs via two key questions: Is a ``typical'' lift of an expander graph also an expander; and how can we (efficiently) construct Ramanujan expanders using lifts? Lately, there has been an increased interest in lifts and their close relation to the notorious Unique Games Conjecture \cite{Kho02}. #R##N#In this paper, we analyze the spectrum of random k-lifts of d-regular graphs. We show that, for random shift $k$-lifts, if all the nontrivial eigenvalues of the base graph G are at most $\lambda$ in absolute value, then with high probability depending only on the number n of nodes of G (and not on k), the absolute value of every nontrivial eigenvalue of the lift is at most $O(\lambda)$. Moreover, if G is moderately expanding, then this bound can be improved to $\lambda+ O(\sqrt{d})$. While previous results on random lifts were asymptotically true with high probability in the degree of the lift k, our result is the first upperbound on spectra of lifts for bounded k. In particular, it implies that a typical small lift of a Ramanujan graph is almost Ramanujan, and we believe it will prove crucial in constructing large Ramanujan expanders of all degrees. We also establish a novel characterization of the spectrum of shift lifts by the spectrum of certain $k$ symmetric matrices, that generalize the signed adjacency matrix (see \cite{BL06}). We believe this characterization is of independent interest.

Includes members:
  Member "the relativized second eigenvalue conjecture of alon":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "find your place simple distributed algorithms for community detection")
  Member "spectral algorithms for unique games":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "efficient algorithms for the potts model on small set expanders")

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.DM(Discrete Mathematics)