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 "non commutative edmonds problem and matrix semi invariants"):
  Abstract: In 1967, Edmonds introduced the problem of computing the rank over the rational function field of an $n\times n$ matrix $T$ with integral homogeneous linear polynomials. In this paper, we consider the non-commutative version of Edmonds' problem: compute the rank of $T$ over the free skew field. It is known that this problem relates to the ring of matrix semi-invariants. In particular, if the nullcone of matrix semi-invariants is defined by elements of degree $\leq \sigma$, then there follows a $\mathrm{poly}(n, \sigma)$-time randomized algorithm to decide whether the non-commutative rank of $T$ is $<n$. To our knowledge, previously the best bound for $\sigma$ was $O(n^2\cdot 4^{n^2})$ over algebraically closed fields of characteristic $0$ (Derksen, 2001). #R##N#In this article we prove the following results: #R##N#(1) We observe that by using an algorithm of Gurvits, and assuming the above bound $\sigma$ for $R(n, m)$ over $\mathbb{Q}$, deciding whether $T$ has non-commutative rank $<n$ over $\mathbb{Q}$ can be done deterministically in time polynomial in the input size and $\sigma$. #R##N#(2) When $\mathbb{F}$ is large enough, we devise a deterministic algorithm for non-commutative Edmonds' problem in time polynomial in $(n+1)!$, with the following consequences. #R##N#(2.a) If the commutative rank and the non-commutative rank of $T$ differ by a constant, then there exists a randomized efficient algorithm that computes the non-commutative rank of $T$. #R##N#(2.b) We prove that $\sigma\leq (n+1)!$. This not only improves the bound obtained from Derksen's work over algebraically closed field of characteristic $0$ but, more importantly, also provides for the first time an explicit bound on $\sigma$ for matrix semi-invariants over fields of positive characteristics.

Includes members:
  Member "operator scaling theory and applications":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "rigorous guarantees for tyler s m estimator via quantum expansion")
  Member "constructive noncommutative rank computation is in deterministic polynomial time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "general linear group action on tensors a candidate for post quantum cryptography")
  Member "on generating the ring of matrix semi invariants":
    also connected through other hyperedges:
      (none)
  Member "generalized wong sequences and their applications to edmonds problems":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "from independent sets and vertex colorings to isotropic spaces and isotropic decompositions")
  Member "geometric complexity theory v equivalence between blackbox derandomization of polynomial identity testing and derandomization of noether s normalization lemma":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "from independent sets and vertex colorings to isotropic spaces and isotropic decompositions")
  Member "deterministic polynomial time algorithms for matrix completion problems":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "general linear group action on tensors a candidate for post quantum cryptography")
  Member "geometric complexity theory ii towards explicit obstructions for embeddings among class varieties":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the computational complexity of plethysm coefficients")

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)