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 "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"):
  Abstract: The celebrated Brascamp-Lieb (BL) inequalities (and their extensions) are an important mathematical tool, unifying and generalizing numerous inequalities in analysis, convex geometry and information theory. While their structural theory is very well understood, far less is known about computing their main parameters. #R##N#We give polynomial time algorithms to compute feasibility of BL-datum, the optimal BL-constant and a weak separation oracle for the BL-polytope. The same result holds for the so-called Reverse BL inequalities of Barthe. The best known algorithms for any of these tasks required at least exponential time. #R##N#The algorithms are obtained by a simple efficient reduction of a given BL-datum to an instance of the Operator Scaling problem defined by Gurvits, for which the present authors have provided a polynomial time algorithm. This reduction implies algorithmic versions of many of the known structural results, and in some cases provide proofs that are different or simpler than existing ones. #R##N#Of particular interest is the fact that the operator scaling algorithm is continuous in its input. Thus as a simple corollary of our reduction we obtain explicit bounds on the magnitude and continuity of the BL-constant in terms of the BL-data. To the best of our knowledge no such bounds were known, as past arguments relied on compactness. The continuity of BL-constants is important for developing non-linear BL inequalities that have recently found so many applications.

Includes members:
  Member "sum of square proof for brascamp lieb type inequality":
    also connected through other hyperedges:
      (none)
  Member "information theoretic perspectives on brascamp lieb inequality and its reverse":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "second order converses via reverse hypercontractivity")
  Member "polynomial time tensor decompositions with sum of squares":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "efficiently learning structured distributions from untrusted batches")
  Member "smoothing brascamp lieb inequalities and strong converses for common randomness generation":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "resolution limits of noisy 20 questions estimation")
  Member "operator scaling theory and applications":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "rigorous guarantees for tyler s m estimator via quantum expansion")
  Member "constructive noncommutative rank computation in deterministic polynomial time over fields of arbitrary characteristics":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on a weighted linear matroid intersection algorithm by deg det computation")
  Member "constructive noncommutative rank computation is in deterministic polynomial time":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "general linear group action on tensors a candidate for post quantum cryptography")
  Member "speeding up sum of squares for tensor decomposition and planted sparse vectors":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "the non convex geometry of low rank matrix optimization")

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)