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 "matrix balancing in lp norms a new analysis of osborne s iteration"):
  Abstract: We study an iterative matrix conditioning algorithm due to Osborne (1960). The goal of the algorithm is to convert a square matrix into a balanced matrix where every row and corresponding column have the same norm. The original algorithm was proposed for balancing rows and columns in the $L_2$ norm, and it works by iterating over balancing a row-column pair in fixed round-robin order. Variants of the algorithm for other norms have been heavily studied and are implemented as standard preconditioners in many numerical linear algebra packages. Recently, Schulman and Sinclair (2015), in a first result of its kind for any norm, analyzed the rate of convergence of a variant of Osborne's algorithm that uses the $L_{\infty}$ norm and a different order of choosing row-column pairs. In this paper we study matrix balancing in the $L_1$ norm and other $L_p$ norms. We show the following results for any matrix $A = (a_{ij})_{i,j=1}^n$, resolving in particular a main open problem mentioned by Schulman and Sinclair. #R##N#1) We analyze the iteration for the $L_1$ norm under a greedy order of balancing. We show that it converges to an $\epsilon$-balanced matrix in $K = O(\min\{\epsilon^{-2}\log w,\epsilon^{-1}n^{3/2}\log(w/\epsilon)\})$ iterations that cost a total of $O(m + Kn\log n)$ arithmetic operations over $O(n\log w)$-bit numbers. Here $m$ is the number of non-zero entries of $A$, and $w = \sum_{i,j} |a_{ij}|/a_{\min}$ with $a_{\min} = \min\{|a_{ij}|:\ a_{ij}\neq 0\}$. #R##N#2) We show that the original round-robin implementation converges to an $\epsilon$-balanced matrix in $O(\epsilon^{-2}n^2\log w)$ iterations totalling $O(\epsilon^{-2}mn\log w)$ arithmetic operations over $O(n\log w)$-bit numbers. #R##N#3) We demonstrate a lower bound of $\Omega(1/\sqrt{\epsilon})$ on the convergence rate of any implementation of the iteration.

Includes members:
  Member "faster parametric shortest path and minimum balance algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "discovering interesting cycles in directed graphs")
  Member "analysis of a classical matrix preconditioning algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "matrix scaling and balancing via box constrained newton s method and interior point methods")

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)