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 "a strong direct product theorem in terms of the smooth rectangle bound"):
  Abstract: A strong direct product theorem states that, in order to solve k instances of a problem, if we provide less than k times the resource required to compute one instance, then the probability of overall success is exponentially small in k. In this paper, we consider the model of two-way public-coin communication complexity and show a strong direct product theorem for all relations in terms of the smooth rectangle bound, introduced by Jain and Klauck as a generic lower bound method in this model. Our result therefore uniformly implies a strong direct product theorem for all relations for which an (asymptotically) optimal lower bound can be provided using the smooth rectangle bound, for example Inner Product, Greater-Than, Set-Disjointness, Gap-Hamming Distance etc. Our result also implies near optimal direct product results for several important functions and relations used to show exponential separations between classical and quantum communication complexity, for which near optimal lower bounds are provided using the rectangle bound, for example by Raz [1999], Gavinsky [2008] and Klartag and Regev [2011]. In fact we are not aware of any relation for which it is known that the smooth rectangle bound does not provide an optimal lower bound. This lower bound subsumes many of the other lower bound methods, for example the rectangle bound (a.k.a the corruption bound), the smooth discrepancy bound (a.k.a the \gamma_2 bound) which in turn subsumes the discrepancy bound, the subdistribution bound and the conditional min-entropy bound. #R##N#We show our result using information theoretic arguments. A key tool we use is a sampling protocol due to Braverman [2012], in fact a modification of it used by Kerenidis, Laplante, Lerays, Roland and Xiao [2012].

Includes members:
  Member "a strong direct product theorem for the tribes function via the smooth rectangle bound":
    also connected through other hyperedges:
      (none)
  Member "lower bounds on information complexity via zero communication protocols and applications":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "query to communication lifting using low discrepancy gadgets")
  Member "information equals amortized communication":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "communication for generating correlation a unifying survey")
  Member "a discrepancy lower bound for information complexity":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "detecting patterns can be hard circuit lower bounds for the string matching problem")
  Member "an optimal lower bound on the communication complexity of gap hamming distance":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "approximate mathbb f _2 sketching of valuation functions")
  Member "strong direct product theorems for quantum communication and query complexity":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a new minimax theorem for randomized algorithms")
  Member "the partition bound for classical communication complexity and query complexity":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "query to communication lifting using low discrepancy gadgets")
  Member "a strong direct product theorem for disjointness":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "query to communication lifting using low discrepancy gadgets")

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.CC(Computational Complexity)