human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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.

Connected through hyperedge HE-1 (induced by source paper "from independent sets and vertex colorings to isotropic spaces and isotropic decompositions"):
  with members:
    - "linear algebraic analogues of the graph isomorphism problem and the erd h o s r enyi model"
    - "algorithms based on algebras and their applications to isomorphism of polynomials with one secret group isomorphism and polynomial identity testing"
    - "the matching problem in general graphs is in quasi nc"
    - "bipartite perfect matching is in quasi nc"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "graph isomorphism in quasipolynomial time"
    - "a deterministic polynomial time algorithm for non commutative rational identity testing"
    - "generalized wong sequences and their applications to edmonds problems"

Connected through hyperedge HE-2 (induced by source paper "derandomization and absolute reconstruction for sums of powers of linear forms"):
  with members:
    - "isomorphism problems for tensors groups and cubic forms completeness and reductions"
    - "orbits of monomials and factorization into products of linear forms"
    - "algorithms based on algebras and their applications to isomorphism of polynomials with one secret group isomorphism and polynomial identity testing"
    - "reconstruction algorithms for sums of affine powers"
    - "a deterministic polynomial time algorithm for non commutative rational identity testing"
    - "quasipolynomial time identity testing of non commutative and read once oblivious algebraic branching programs"
    - "symmetric tensor decomposition"

Connected through hyperedge HE-3 (induced by source paper "operator scaling via geodesically convex optimization invariant theory and polynomial identity testing"):
  with members:
    - "alternating minimization scaling algorithms and the null cone problem from invariant theory"
    - "algorithms based on algebras and their applications to isomorphism of polynomials with one secret group isomorphism and polynomial identity testing"
    - "the paulsen problem continuous operator scaling and smoothed analysis"
    - "much faster algorithms for matrix scaling"
    - "matrix scaling and balancing via box constrained newton s method and interior point methods"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "operator scaling theory and applications"
    - "constructive noncommutative rank computation in deterministic polynomial time over fields of arbitrary characteristics"

Connected through hyperedge HE-4 (induced by source paper "recent progress on scaling algorithms and applications"):
  with members:
    - "the paulsen problem continuous operator scaling and smoothed analysis"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "operator scaling theory and applications"
    - "constructive noncommutative rank computation is in deterministic polynomial time"
    - "explicit lower bounds via geometric complexity theory"
    - "geometric complexity theory and tensor rank"

Connected through hyperedge HE-5 (induced by source paper "alternating minimization scaling algorithms and the null cone problem from invariant theory"):
  with members:
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "operator scaling theory and applications"
    - "understanding alternating minimization for matrix completion"
    - "explicit lower bounds via geometric complexity theory"
    - "geometric complexity theory v equivalence between blackbox derandomization of polynomial identity testing and derandomization of noether s normalization lemma"

Connected through hyperedge HE-6 (induced by source paper "interactions of computational complexity theory and mathematics"):
  with members:
    - "no occurrence obstructions in geometric complexity theory"
    - "algorithmic and optimization aspects of brascamp lieb inequalities via operator scaling"
    - "uniform sampling through the lov asz local lemma"
    - "approximate counting the lovasz local lemma and inference in graphical models"
    - "graph isomorphism in quasipolynomial time"
    - "operator scaling theory and applications"
    - "analysis of boolean functions"
    - "explicit noether normalization for simultaneous conjugation via polynomial identity testing"

Connected through hyperedge HE-7 (induced by source paper "linear algebraic analogues of the graph isomorphism problem and the erd h o s r enyi model"):
  with members:
    - "algorithms based on algebras and their applications to isomorphism of polynomials with one secret group isomorphism and polynomial identity testing"
    - "on the group and color isomorphism problems"
    - "graph isomorphism in quasipolynomial time"
    - "a deterministic polynomial time algorithm for non commutative rational identity testing"
    - "bidirectional collision detection and faster deterministic isomorphism testing"
    - "practical graph isomorphism ii"
    - "deterministic polynomial time algorithms for matrix completion problems"

Connected through hyperedge HE-8 (induced by source paper "algorithms based on algebras and their applications to isomorphism of polynomials with one secret group isomorphism and polynomial identity testing"):
  with members:
    - "a deterministic polynomial time algorithm for non commutative rational identity testing"
    - "progress on polynomial identity testing ii"
    - "solving the isomorphism of polynomials with two secrets problem for all pairs of quadratic forms"
    - "algorithms for group isomorphism via group extensions and cohomology"
    - "deterministic polynomial time algorithms for matrix completion problems"

Question: Please tell me which class the center node 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)