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 "high dimensional discrete integration by hashing and optimization"):
  Abstract: Recently Ermon et al. (2013) pioneered an ingenuous way to practically compute approximations to large scale counting or discrete integration problems by using random hashes. The hashes are used to reduce the counting problems into many separate discrete optimization problems. The optimization problems can be solved by an NP-oracle, and if they allow some amenable structure then commercial SAT solvers or linear programming (LP) solvers can be used in lieu of the NP-oracle. In particular, Ermon et al. has shown that if the domain of integration is $\{0,1\}^n$ then it is possible to obtain a $16$-approximation by this technique. #R##N#In many crucial counting tasks, such as computation of partition function of ferromagnetic Potts model, the domain of integration is naturally $\{0,1,\dots, q-1\}^n, q>2$. A straightforward extension of Ermon et al.'s work would allow a $q^2$-approximation for this problem, assuming the existence of an optimization oracle. In this paper, we show that it is possible to obtain a $(2+\frac2{q-1})^2$-approximation to the discrete integration problem, when $q$ is a power of an odd prime (a similar expression follows for even $q$). We are able to achieve this by using an idea of optimization over multiple bins of the hash functions, that can be easily implemented by inequality constraints, or even in unconstrained way. Also the burden on the NP-oracle is not increased by our method (an LP solver can still be used). Furthermore, we provide a close-to-4-approximation for the permanent of a matrix by extending our technique. Note that, the domain of integration here is the symmetric group. Finally, we provide memory optimal hash functions that uses minimal number of random bits for the above purpose. We are able to obtain these structured hashes without sacrificing the amenability of the NP-oracle. We provide experimental simulation results to support our algorithms.

Includes members:
  Member "optimization with parity constraints from binary codes to discrete integration":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "quantitative verification of neural networks and its security applications")
  Member "an approximation algorithm for k sat":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "fine grained reductions from approximate counting to decision")

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)