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 "computational complexity of certifying restricted isometry property"):
  Abstract: Given a matrix $A$ with $n$ rows, a number $k<n$, and $0<\delta < 1$, $A$ is $(k,\delta)$-RIP (Restricted Isometry Property) if, for any vector $x \in \mathbb{R}^n$, with at most $k$ non-zero co-ordinates, $$(1-\delta) \|x\|_2 \leq \|A x\|_2 \leq (1+\delta)\|x\|_2$$ In many applications, such as compressed sensing and sparse recovery, it is desirable to construct RIP matrices with a large $k$ and a small $\delta$. Given the efficacy of random constructions in generating useful RIP matrices, the problem of certifying the RIP parameters of a matrix has become important. #R##N#In this paper, we prove that it is hard to approximate the RIP parameters of a matrix assuming the Small-Set-Expansion-Hypothesis. Specifically, we prove that for any arbitrarily large constant $C>0$ and any arbitrarily small constant $0<\delta<1$, there exists some $k$ such that given a matrix $M$, it is SSE-Hard to distinguish the following two cases: #R##N#- (Highly RIP) $M$ is $(k,\delta)$-RIP. #R##N#- (Far away from RIP) $M$ is not $(k/C, 1-\delta)$-RIP. #R##N#Most of the previous results on the topic of hardness of RIP certification only hold for certification when $\delta=o(1)$. In practice, it is of interest to understand the complexity of certifying a matrix with $\delta$ being close to $\sqrt{2}-1$, as it suffices for many real applications to have matrices with $\delta = \sqrt{2}-1$. Our hardness result holds for any constant $\delta$. Specifically, our result proves that even if $\delta$ is indeed very small, i.e. the matrix is in fact \emph{strongly RIP}, certifying that the matrix exhibits \emph{weak RIP} itself is SSE-Hard. #R##N#In order to prove the hardness result, we prove a variant of the Cheeger's Inequality for sparse vectors.

Includes members:
  Member "hidden cliques and the certification of the restricted isometry property":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the average case complexity of counting cliques in erdos renyi hypergraphs")
  Member "on the certification of the restricted isometry property":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "hidden cliques and the certification of the restricted isometry property")
  Member "reductions between expansion problems":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "bisect and conquer hierarchical clustering via max uncut bisection")

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)