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 "approximating the expansion profile and almost optimal local graph clustering"):
  Abstract: Spectral partitioning is a simple, nearly-linear time, algorithm to find sparse cuts, and the Cheeger inequalities provide a worst-case guarantee for the quality of the approximation found by the algorithm. Local graph partitioning algorithms [ST08,ACL06,AP09] run in time that is nearly linear in the size of the output set, and their approximation guarantee is worse than the guarantee provided by the Cheeger inequalities by a polylogarithmic $\log^{\Omega(1)} n$ factor. It has been a long standing open problem to design a local graph clustering algorithm with an approximation guarantee close to the guarantee of the Cheeger inequalities and with a running time nearly linear in the size of the output. #R##N#In this paper we solve this problem; we design an algorithm with the same guarantee (up to a constant factor) as the Cheeger inequality, that runs in time slightly super linear in the size of the output. This is the first sublinear (in the size of the input) time algorithm with almost the same guarantee as the Cheeger's inequality. As a byproduct of our results, we prove a bicriteria approximation algorithm for the expansion profile of any graph. Let $\phi(\gamma) = \min_{\mu(S) \leq \gamma}\phi(S)$. There is a polynomial time algorithm that, for any $\gamma,\epsilon>0$, finds a set $S$ of measure $\mu(S)\leq 2\gamma^{1+\epsilon}$, and expansion $\phi(S)\leq \sqrt{2\phi(\gamma)/\epsilon}$. Our proof techniques also provide a simpler proof of the structural result of Arora, Barak, Steurer [ABS10], that can be applied to irregular graphs. #R##N#Our main technical tool is that for any set $S$ of vertices of a graph, a lazy $t$-step random walk started from a randomly chosen vertex of $S$, will remain entirely inside $S$ with probability at least $(1-\phi(S)/2)^t$. This itself provides a new lower bound to the uniform mixing time of any finite states reversible markov chain.

Includes members:
  Member "min max graph partitioning and small set expansion":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "planted models for k way edge and vertex expansion")
  Member "approximating the exponential the lanczos method and an tilde o m time spectral algorithm for balanced separator":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a deterministic algorithm for balanced cut with applications to dynamic connectivity flows and beyond")
  Member "a local clustering algorithm for massive graphs and its application to nearly linear time graph partitioning":
    also connected through other hyperedges:
      - Hyperedge HE-3 (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-4 (induced by source paper "deterministic graph cuts in subquadratic time sparse balanced and k vertex")
  Member "nearly linear time algorithms for graph partitioning graph sparsification and solving linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "compressive sensing for cut improvement and local clustering")

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)