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 "the distribution function of the longest path length in constant treewidth dags with random edge length"):
  Abstract: This paper is about the length $X_{\rm MAX}$ of the longest path in directed acyclic graph (DAG) $G=(V,E)$ that have random edge lengths, where $|V|=n$ and $|E|=m$. Especially, when the edge lengths are mutually independent and uniformly distributed, the problem of computing the distribution function $\Pr[X_{\rm MAX}\le x]$ is known to be $\#P$-hard even in case $G$ is a directed path. This is because $\Pr[X_{\rm MAX}\le x]$ is equal to the volume of the knapsack polytope, an $m$-dimensional unit hypercube truncated by a halfspace. In this paper, we show that there is a {\em deterministic} fully polynomial time approximation scheme (FPTAS) for computing $\Pr[X_{\rm MAX}\le x]$ in case the treewidth of $G$ is bounded by a constant $k$; where there may be exponentially many source-terminal paths in $G$. The running time of our algorithm is $O(n(\frac{2mn}{\epsilon})^{k^2+4k})$ to achieve a multiplicative approximation ratio $1+\epsilon$. On the way to show our FPTAS, we show a fundamental formula that represents $\Pr[X_{\rm MAX}\le x]$ by $n-1$ repetition of definite integrals. This also leads us to more results. In case the edge lengths obey the mutually independent standard exponential distribution, we show that there exists an $(2kmn)^{O(k)}$ time exact algorithm. We also show, for random edge lengths satisfying certain conditions, that computing $\Pr[X_{\rm MAX}\le x]$ is fixed parameter tractable if we choose treewidth $k$, the additive error $\epsilon'$ and $x$ as the parameters by using the Taylor approximation.

Includes members:
  Member "a fully polynomial time approximation scheme for approximating a sum of random variables":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "an fptas for stochastic unbounded min knapsack problem")
  Member "polynomial time approximation schemes for knapsack and related counting problems using branching programs":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "an fptas for the volume of a cal v polytope it is hard to compute the volume of the intersection of two cross polytopes")

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.CC(Computational Complexity)