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 "fast hamiltonicity checking via bases of perfect matchings"):
  Abstract: For an even integer t \geq 2, the Matchings Connecivity matrix H_t is a matrix that has rows and columns both labeled by all perfect matchings of the complete graph K_t on t vertices; an entry H_t[M_1,M_2] is 1 if M_1\cup M_2 is a Hamiltonian cycle and 0 otherwise. Motivated by the computational study of the Hamiltonicity problem, we present three results on the structure of H_t: We first show that H_t has rank at most 2^{t/2-1} over GF(2) via an appropriate factorization that explicitly provides families of matchings X_t forming bases for H_t. Second, we show how to quickly change representation between such bases. Third, we notice that the sets of matchings X_t induce permutation matrices within H_t. #R##N#Subsequently, we use the factorization to obtain an 1.888^n n^{O(1)} time Monte Carlo algorithm that solves the Hamiltonicity problem in directed bipartite graphs. Our algorithm as well counts the number of Hamiltonian cycles modulo two in directed bipartite or undirected graphs in the same time bound. Moreover, we use the fast basis change algorithm from the second result to present a Monte Carlo algorithm that given an undirected graph on n vertices along with a path decomposition of width at most pw decides Hamiltonicity in (2+\sqrt{2})^{pw}n^{O(1)} time. Finally, we use the third result to show that for every \epsilon >0 this cannot be improved to (2+\sqrt{2}-\epsilon)^{pw}n^{O(1)} time unless the Strong Exponential Time Hypothesis fails, i.e., a faster algorithm for this problem would imply the breakthrough result of a (2-\epsilon)^n time algorithm for CNF-Sat.

Includes members:
  Member "on problems as hard as cnf sat":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "solving weighted and counting variants of connectivity problems parameterized by treewidth deterministically in single exponential time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "representative sets of product families")
  Member "solving connectivity problems parameterized by treewidth in single exponential time":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "hamiltonian cycle parameterized by treedepth in single exponential time and polynomial space")
  Member "determinant sums for undirected hamiltonicity":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "finding temporal patterns using algebraic fingerprints")
  Member "known algorithms on graphs of bounded treewidth are probably optimal":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the complexity of finding large odd induced subgraphs and odd colorings")
  Member "trimmed moebius inversion and graphs of bounded degree":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "finding hamiltonian cycle in graphs of bounded treewidth experimental evaluation")
  Member "the traveling salesman problem for cubic graphs":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "an exact algorithm for tsp in degree 3 graphs via circuit procedure and amortization on connectivity structure")

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)