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 "equivalence of systematic linear data structures and matrix rigidity"):
  Abstract: Recently, Dvir, Golovnev, and Weinstein have shown that sufficiently strong lower bounds for linear data structures would imply new bounds for rigid matrices. However, their result utilizes an algorithm that requires an $NP$ oracle, and hence, the rigid matrices are not explicit. In this work, we derive an equivalence between rigidity and the systematic linear model of data structures. For the $n$-dimensional inner product problem with $m$ queries, we prove that lower bounds on the query time imply rigidity lower bounds for the query set itself. In particular, an explicit lower bound of $\omega\left(\frac{n}{r}\log m\right)$ for $r$ redundant storage bits would yield better rigidity parameters than the best bounds due to Alon, Panigrahy, and Yekhanin. We also prove a converse result, showing that rigid matrices directly correspond to hard query sets for the systematic linear model. As an application, we prove that the set of vectors obtained from rank one binary matrices is rigid with parameters matching the known results for explicit sets. This implies that the vector-matrix-vector problem requires query time $\Omega(n^{3/2}/r)$ for redundancy $r \geq \sqrt{n}$ in the systematic linear model, improving a result of Chakraborty, Kamma, and Larsen. Finally, we prove a cell probe lower bound for the vector-matrix-vector problem in the high error regime, improving a result of Chattopadhyay, Koucký, Loff, and Mukhopadhyay.

Includes members:
  Member "static data structure lower bounds imply rigidity":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "tight static lower bounds for non adaptive data structures")
  Member "matrix rigidity and the croot lev pach lemma":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the generalized orthogonality dimension of generalized kneser graphs bounds and applications")
  Member "crossing the logarithmic barrier for dynamic boolean data structure lower bounds":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "probabilistic rank and matrix rigidity":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the generalized orthogonality dimension of generalized kneser graphs bounds and applications")
  Member "unifying and strengthening hardness for dynamic problems via the online matrix vector multiplication conjecture":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")
  Member "new unconditional hardness results for dynamic and online problems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "dynamic matrix inverse improved algorithms and matching conditional lower bounds")
  Member "adapt or die polynomial lower bounds for non adaptive dynamic data structures":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "an adaptive step toward the multiphase conjecture")
  Member "min rank conjecture for log depth circuits":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "static data structure lower bounds imply rigidity")

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)