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 "algorithms for group isomorphism via group extensions and cohomology"):
  Abstract: The isomorphism problem for groups given by multiplication tables (GpI) is well-known to be solvable in n^O(log n) time, but only recently has there been significant progress. For example, in 2012 Babai et al. gave a polynomial-time algorithm for groups with no abelian normal subgroups. Thus it is crucial to understand groups with abelian normal subgroups to develop n^o(log n)-time algorithms. #R##N#We advocate a strategy via the extension theory of groups, which describes how a normal subgroup N is related to G/N via G. This strategy "splits" GpI into two subproblems: one on group actions and one on group cohomology. The solution of these problems is essentially necessary and sufficient to solve GpI. Previous works naturally align with this strategy, and it thus helps explain in a unified way the recent successes on other group classes. In particular, most results in the Cayley table model focus on the group action aspect, despite the general necessity of cohomology. #R##N#To make progress on the cohomology aspect we consider central-radical groups, proposed by Babai et al.: groups whose solvable normal subgroups are contained in the center. (Babai et al. considered groups with no solvable normal subgroups.) Following the above strategy, we solve GpI in n^O(log log n) time for central-radical groups, and in polynomial time for several prominent subclasses of central-radical groups. We achieve the same time bounds for groups whose solvable normal subgroups are elementary abelian but not central. #R##N#Prior to our work, the easy n^O(log n) algorithm was the best known even for groups with a central radical of size 2. We use several mathematical results on the detailed structure of cohomology classes, as well as algorithms for code equivalence, coset intersection and cyclicity testing of modules over finite-dimensional algebras. We also suggest several promising directions for future work.

Includes members:
  Member "bidirectional collision detection and faster deterministic isomorphism testing":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "isomorphism problems for tensors groups and cubic forms completeness and reductions")
  Member "complexity classes of equivalence problems revisited":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "isomorphism problems for tensors groups and cubic forms completeness and reductions")
  Member "lie algebra conjugacy":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "isomorphism problems for tensors groups and cubic forms completeness and reductions")
  Member "deterministic polynomial time algorithms for matrix completion problems":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "general linear group action on tensors a candidate for post quantum cryptography")
  Member "efficient isomorphism testing for a class of group extensions":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the group and color isomorphism problems")

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)