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 "minimum d dimensional arrangement with fixed points"):
  Abstract: In the Minimum $d$-Dimensional Arrangement Problem (d-dimAP) we are given a graph with edge weights, and the goal is to find a 1-1 map of the vertices into $\mathbb{Z}^d$ (for some fixed dimension $d\geq 1$) minimizing the total weighted stretch of the edges. This problem arises in VLSI placement and chip design. #R##N#Motivated by these applications, we consider a generalization of d-dimAP, where the positions of some of the vertices (pins) is fixed and specified as part of the input. We are asked to extend this partial map to a map of all the vertices, again minimizing the weighted stretch of edges. This generalization, which we refer to as d-dimAP+, arises naturally in these application domains (since it can capture blocked-off parts of the board, or the requirement of power-carrying pins to be in certain locations, etc.). Perhaps surprisingly, very little is known about this problem from an approximation viewpoint. #R##N#For dimension $d=2$, we obtain an $O(k^{1/2} \cdot \log n)$-approximation algorithm, based on a strengthening of the spreading-metric LP for 2-dimAP. The integrality gap for this LP is shown to be $\Omega(k^{1/4})$. We also show that it is NP-hard to approximate 2-dimAP+ within a factor better than $\Omega(k^{1/4-\eps})$. We also consider a (conceptually harder, but practically even more interesting) variant of 2-dimAP+, where the target space is the grid $\mathbb{Z}_{\sqrt{n}} \times \mathbb{Z}_{\sqrt{n}}$, instead of the entire integer lattice $\mathbb{Z}^2$. For this problem, we obtain a $O(k \cdot \log^2{n})$-approximation using the same LP relaxation. We complement this upper bound by showing an integrality gap of $\Omega(k^{1/2})$, and an $\Omega(k^{1/2-\eps})$-inapproximability result. #R##N#Our results naturally extend to the case of arbitrary fixed target dimension $d\geq 1$.

Includes members:
  Member "vertex sparsifiers new results from old techniques":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "scattering and sparse partitions and their applications")
  Member "reductions between expansion problems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (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.DS(Data Structures and Algorithms)