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 "dynamic set cover improved algorithms lower bounds"):
  Abstract: Set cover is a classic problem in combinatorial optimization where a set of $n$ elements have to be covered by a minimum number of subsets from a given collection of size $m$. The two traditional lines of inquiry for this problem are via greedy and primal dual algorithms, and respectively yield (tight) approximation factors of $\ln n$, where $n$ is the total number of elements, and $f$, where every element belongs to at most $f$ sets. Recent research has focused on the dynamic setting, where the set of elements changes over time. Using the same lines of inquiry, this has led to the following results: (a) an $O(\log n)$-approximation in $O(f \log n)$ (amortized) update time (Gupta {\em et al.}, STOC 2017), and (b) an $O(f^2)$-approximation in $O(f \log (m+n))$ (amortized) update time (Bhattacharya {\em et al.}, ICALP 2015). While the former result matches the offline approximation within a constant factor, the latter does not; indeed, the only $O(f)$-approximation known in the dynamic setting is by re-solving the problem after every update. #R##N#In this paper, we show that it is possible to maintain efficiently a solution (almost) as good as the primal-dual offline one: we give a $(1+\epsilon) f$-approximation for set cover in $O(f^2\log n/\epsilon)$ (amortized) update time. If we are in a decremental setting, i.e., there are element deletions but no insertions, the update time can be improved to $O(f^2/\epsilon)$, while still obtaining an $(1+\epsilon) f$-approximation. Finally, we study the dependence of the update time on $f$. Using the recent distributed PCP-framework, we show that any dynamic algorithm for set cover that has an amortized update time of $O(f^{1-\epsilon})$ must have an approximation factor that is $\Omega(n^\delta)$ for some $\delta>0$ under the Strong Exponential Time Hypothesis.

Includes members:
  Member "fully dynamic mis in uniformly sparse graphs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "explicit and implicit dynamic coloring of graphs with bounded arboricity")
  Member "fully dynamic maximal independent set with sublinear update time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "hardness of approximate nearest neighbor search":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the i o complexity of the k nearest neighbor problem")
  Member "on the hardness of approximate and exact bichromatic maximum inner product":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "approximating subset sum is equivalent to min plus convolution")
  Member "tight bounds on the round complexity of the distributed maximum coverage problem":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "equivalence classes and conditional hardness in massively parallel computations")
  Member "distributed pcp theorems for hardness of approximation in p":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "graphs cannot be indexed in polynomial time for sub quadratic time string matching unless seth fails")
  Member "dynamic algorithms for graph coloring":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "decremental single source reachability in planar digraphs":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")

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)