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 "on nondeterministic derandomization of freivalds algorithm consequences avenues and algorithmic progress"):
  Abstract: Motivated by studying the power of randomness, certifying algorithms and barriers for fine-grained reductions, we investigate the question whether the multiplication of two $n\times n$ matrices can be performed in near-optimal nondeterministic time $\tilde{O}(n^2)$. Since a classic algorithm due to Freivalds verifies correctness of matrix products probabilistically in time $O(n^2)$, our question is a relaxation of the open problem of derandomizing Freivalds' algorithm. #R##N#We discuss consequences of a positive or negative resolution of this problem and provide potential avenues towards resolving it. Particularly, we show that sufficiently fast deterministic verifiers for 3SUM or univariate polynomial identity testing yield faster deterministic verifiers for matrix multiplication. Furthermore, we present the partial algorithmic progress that distinguishing whether an integer matrix product is correct or contains between 1 and $n$ erroneous entries can be performed in time $\tilde{O}(n^2)$ -- interestingly, the difficult case of deterministic matrix product verification is not a problem of "finding a needle in the haystack", but rather cancellation effects in the presence of many errors. #R##N#Our main technical contribution is a deterministic algorithm that corrects an integer matrix product containing at most $t$ errors in time $\tilde{O}(\sqrt{t} n^2 + t^2)$. To obtain this result, we show how to compute an integer matrix product with at most $t$ nonzeroes in the same running time. This improves upon known deterministic output-sensitive integer matrix multiplication algorithms for $t = \Omega(n^{2/3})$ nonzeroes, which is of independent interest.

Includes members:
  Member "error correction in fast matrix multiplication and inverse":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "lu factorization with errors")
  Member "near optimal linear decision trees for k sum and related problems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "all non trivial variants of 3 ldt are equivalent")
  Member "strong eth breaks with merlin and arthur short non interactive proofs of batch evaluation":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "new algorithms and lower bounds for all pairs max flow in undirected graphs")
  Member "threesomes degenerates and love triangles":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the fine grained complexity of parity problems")
  Member "powers of tensors and fast matrix multiplication":
    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 "popular conjectures imply strong lower bounds for dynamic problems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")
  Member "3sum 3xor triangles":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "all non trivial variants of 3 ldt are equivalent")
  Member "faster all pairs shortest paths via circuit complexity":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "deterministic algorithms for decremental approximate shortest paths faster and simpler")

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)