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 "placement and allocation of virtual network functions multi dimensional case"):
  Abstract: Network function virtualization (NFV) is an emerging design paradigm that replaces physical middlebox devices with software modules running on general purpose commodity servers. While gradually transitioning to NFV, Internet service providers face the problem of where to introduce NFV in order to make the most benefit of that; here, we measure the benefit by the amount of traffic that can be serviced through the NFV. This problem is non-trivial as it is composed of two challenging subproblems: 1) placement of nodes to support virtual network functions (referred to as VNF-nodes); and 2) allocation of the VNF-nodes resources to network flows. This problem has been studied recently but for the one-dimensional setting, where all network flows require one network function, which requires a unit of resource to process a unit of flow. In this work, we extend to the multi-dimensional setting, where flows can require multiple network functions, which can also require a different amount of each resource to process a unit of flow. The multi-dimensional setting introduces new challenges in addition to those of the one-dimensional setting (e.g., NP-hardness and non-submodularity) and also makes the resource allocation a multi-dimensional generalization of the generalized assignment problem with assignment restrictions. To address these difficulties, we propose a novel two-level relaxation method and utilize the primal-dual technique to design two approximation algorithms that achieve an approximation ratio of $\frac{(e-1)(Z-1) } {2 e^2 Z (kR)^{1/(Z-1)}}$ and $\frac{(e-1)(Z-1)}{2e(Z-1+e Z R^{1/(Z-1)})}$, where $k$ (resp. $R$) is the number of VNF-nodes (resp. resources), and $Z$ is a measure of the available resource compared to flow demand. Finally, we perform extensive trace-driven simulations to show the effectiveness of the proposed algorithms.

Includes members:
  Member "joint placement and allocation of virtual network functions with budget and capacity constraints":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "online joint placement and allocation of virtual network functions with heterogeneous servers")
  Member "shortest path and maximum flow problems under service function chaining constraints":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "online joint placement and allocation of virtual network functions with heterogeneous servers")
  Member "provably efficient algorithms for joint placement and allocation of virtual network functions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "online joint placement and allocation of virtual network functions with heterogeneous servers")
  Member "approximate and incremental network function placement":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "online joint placement and allocation of virtual network functions with heterogeneous servers")
  Member "string submodular functions with curvature constraints":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "adaptive sequence submodularity")
  Member "online admission control and embedding of service chains":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "robust online composition routing and nf placement for nfv enabled services")
  Member "competitive and deterministic embeddings of virtual networks":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "robust online composition routing and nf placement for nfv enabled services")
  Member "maximizing sequence submodular functions and its application to online advertising":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "adaptive sequence submodularity")

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.NI(Networking and Internet Architecture)