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 "directed hamiltonicity and out branchings via generalized laplacians"):
  Abstract: We are motivated by a tantalizing open question in exact algorithms: can we detect whether an $n$-vertex directed graph $G$ has a Hamiltonian cycle in time significantly less than $2^n$? We present new randomized algorithms that improve upon several previous works: #R##N#1. We show that for any constant $0<\lambda<1$ and prime $p$ we can count the Hamiltonian cycles modulo $p^{\lfloor (1-\lambda)\frac{n}{3p}\rfloor}$ in expected time less than $c^n$ for a constant $c<2$ that depends only on $p$ and $\lambda$. Such an algorithm was previously known only for the case of counting modulo two [Bj\"orklund and Husfeldt, FOCS 2013]. #R##N#2. We show that we can detect a Hamiltonian cycle in $O^*(3^{n-\alpha(G)})$ time and polynomial space, where $\alpha(G)$ is the size of the maximum independent set in $G$. In particular, this yields an $O^*(3^{n/2})$ time algorithm for bipartite directed graphs, which is faster than the exponential-space algorithm in [Cygan et al., STOC 2013]. #R##N#Our algorithms are based on the algebraic combinatorics of "incidence assignments" that we can capture through evaluation of determinants of Laplacian-like matrices, inspired by the Matrix--Tree Theorem for directed graphs. In addition to the novel algorithms for directed Hamiltonicity, we use the Matrix--Tree Theorem to derive simple algebraic algorithms for detecting out-branchings. Specifically, we give an $O^*(2^k)$-time randomized algorithm for detecting out-branchings with at least $k$ internal vertices, improving upon the algorithms of [Zehavi, ESA 2015] and [Bj\"orklund et al., ICALP 2015]. We also present an algebraic algorithm for the directed $k$-Leaf problem, based on a non-standard monomial detection problem.

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 "spotting trees with few leaves":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "designing deterministic polynomial space algorithms by color coding multivariate polynomials")
  Member "fast algorithms for parameterized problems with relaxed disjointness constraints":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "time and space optimal algorithms for the many visits tsp")
  Member "mixing color coding related techniques":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "parameterized complexity of partial scheduling")
  Member "faster exponential time algorithms in graphs of bounded average degree":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a faster hafnian formula for complex matrices and its benchmarking on the titan supercomputer")
  Member "the parity of directed hamiltonian cycles":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "a tight lower bound for counting hamiltonian cycles via matrix rank")
  Member "a new direction for counting perfect matchings":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on symbolic approaches for computing the matrix permanent")
  Member "below all subsets for some permutational counting problems":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "sfcm r a novel algorithm for the hamiltonian sequence problem")

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)