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 "maximizing the number of spanning trees in a connected graph"):
  Abstract: We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: #R##N#- We give a greedy algorithm that, using submodularity, obtains an approximation ratio of $(1 - 1/e - \epsilon)$ in the exponent of the number of spanning trees for any $\epsilon > 0$ in time $\tilde{O}(m \epsilon^{-1} + (n + q) \epsilon^{-3})$, where $m$ and $q$ is the number of edges in the original graph and the candidate edge set, respectively. Our running time is optimal with respect to the input size up to logarithmic factors, and substantially improves upon the $O(n^3)$ running time of the previous proposed greedy algorithm with approximation ratio $(1 - 1/e)$ in the exponent. Notably, the independence of our running time of $k$ is novel, comparing to conventional top-$k$ selections on graphs that usually run in $\Omega(mk)$ time. A key ingredient of our greedy algorithm is a routine for maintaining effective resistances under edge additions in an online-offline hybrid setting. #R##N#- We show the exponential inapproximability of this problem by proving that there exists a constant $c > 0$ such that it is NP-hard to approximate the optimum number of spanning trees in the exponent within $(1 - c)$. This inapproximability result follows from a reduction from the minimum path cover in undirected graphs, whose hardness again follows from the constant inapproximability of the Traveling Salesman Problem (TSP) with distances 1 and 2. Thus, the approximation ratio of our algorithm is also optimal up to a constant factor in the exponent. To our knowledge, this is the first hardness of approximation result for maximizing the number of spanning trees in a graph, or equivalently, by Kirchhoff's matrix-tree theorem, maximizing the determinant of an SDDM matrix.

Includes members:
  Member "current flow group closeness centrality for complex networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a distributed laplacian solver and its applications to electrical flow and random spanning tree computation")
  Member "fully dynamic spectral vertex sparsifiers and applications":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "solving tall dense linear programs in nearly linear time")
  Member "kirchhoff index as a measure of edge centrality in weighted networks nearly linear time algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "fully dynamic spectral vertex sparsifiers and applications")
  Member "graph sparsification spectral sketches and faster resistance computation via short cycle decompositions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a deterministic algorithm for balanced cut with applications to dynamic connectivity flows and beyond")
  Member "a nearly linear time algorithm for submodular maximization with a knapsack constraint":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximability of monotone submodular function maximization under cardinality and matroid constraints in the streaming model")
  Member "an almost linear time algorithm for uniform random spanning tree generation":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "subdeterminant maximization via nonconvex relaxations and anti concentration":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "composable core sets for determinant maximization a simple near optimal algorithm")
  Member "determinant preserving sparsification of sddm matrices with applications to counting and sampling spanning trees":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "fully dynamic spectral vertex sparsifiers and applications")

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)