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 "improved cheeger s inequality and analysis of local graph partitioning using vertex expansion and expansion profile"):
  Abstract: We prove two generalizations of the Cheeger's inequality. The first generalization relates the second eigenvalue to the edge expansion and the vertex expansion of the graph G, $\lambda_2 = \Omega(\phi^V(G) \phi(G))$, where $\phi^V(G)$ denotes the robust vertex expansion of G and $\phi(G)$ denotes the edge expansion of G. The second generalization relates the second eigenvalue to the edge expansion and the expansion profile of G, for all $k \ge 2$, $\lambda_2 = \Omega(\phi_k(G) \phi(G) / k)$, where $\phi_k(G)$ denotes the k-way expansion of G. These show that the spectral partitioning algorithm has better performance guarantees when $\phi^V(G)$ is large (e.g. planted random instances) or $\phi_k(G)$ is large (instances with few disjoint non-expanding sets). Both bounds are tight up to a constant factor. #R##N#Our approach is based on a method to analyze solutions of Laplacian systems, and this allows us to extend the results to local graph partitioning algorithms. In particular, we show that our approach can be used to analyze personal pagerank vectors, and to give a local graph partitioning algorithm for the small-set expansion problem with performance guarantees similar to the generalizations of Cheeger's inequality. We also present a spectral approach to prove similar results for the truncated random walk algorithm. These show that local graph partitioning algorithms almost match the performance of the spectral partitioning algorithm, with the additional advantages that they apply to the small-set expansion problem and their running time could be sublinear. Our techniques provide common approaches to analyze the spectral partitioning algorithm and local graph partitioning algorithms.

Includes members:
  Member "local graph clustering beyond cheeger s inequality":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "local network community detection with continuous optimization of conductance and weighted kernel k means")
  Member "improved cheeger s inequality analysis of spectral partitioning algorithms through higher order spectral gap":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "efficient algorithms for the potts model on small set expanders")
  Member "many sparse cuts via higher eigenvalues":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "planted models for k way edge and vertex expansion")
  Member "approximating the expansion profile and almost optimal local graph clustering":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "efficient algorithms for the potts model on small set expanders")
  Member "a local clustering algorithm for massive graphs and its application to nearly linear time graph partitioning":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "compressive sensing for cut improvement and local clustering")
  Member "finding sparse cuts locally using evolving sets":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "deterministic graph cuts in subquadratic time sparse balanced and k vertex")

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.DS(Data Structures and Algorithms)