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 "new bounds on augmenting steps of block structured integer programs"):
  Abstract: We consider 4-block $n$-fold integer programs, whose constraint matrix consists of $n$ copies of small matrices $A$, $B$, and $D$, and one copy of $C$, in a specific block structure. All existing algorithms along this line of research follows an iterative augmentation framework, which relies on the so-called Graver basis of the constraint matrix that constitutes a set of fundamental augmenting steps. Bounding the $\ell_1$- or $\ell_\infty$-norm of elements of the Graver basis is the key to these algorithms. Hemmecke et al.~[Math. Prog. 2014] showed that 4-block $n$-fold IP has Graver elements of $\ell_\infty$-norm at most $O_{FPT}(n^{2^{s_{D}}})$, leading to an algorithm with a similar runtime; here, $s_{D}$ is the number of rows of matrix $D$ and $ O_{FPT}(1)$ hides a multiplicative factor that is only dependent on the small matrices $A,B,C,D$. #R##N#We prove that the $\ell_{\infty}$-norm of the Graver elements of 4-block $n$-fold IP is upper bounded by $O_{FPT}(n^{s_{D}})$, improving significantly over the previous bound $O_{FPT} (n^{2^{s_{D}}})$. We also provide a matching lower bound of $\Omega(n^{s_{D}})$ which even holds for arbitrary non-zero lattice elements, ruling out augmenting algorithm relying on even more restricted notions of augmentation than the Graver basis. We then consider a special case of 4-block $n$-fold in which $C$ is a zero matrix, called 3-block $n$-fold IP. We show that while even there the $\ell_{\infty}$-norm of its Graver elements is $\Omega(n^{s_{D}})$, there exists a different decomposition into lattice elements whose $\ell_{\infty}$-norm is bounded by $ O_{FPT}(1)$, which allows us to provide improved upper bounds on the $\ell_{\infty}$-norm of Graver elements for 3-block $n$-fold IP.

Includes members:
  Member "a parameterized strongly polynomial algorithm for block structured integer programs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "n fold integer programming via lp rounding")
  Member "faster algorithms for integer programs with block structure":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "n fold integer programming via lp rounding")
  Member "empowering the configuration ip new ptas results for scheduling with setups times":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "n fold integer programming via lp rounding")
  Member "on integer programming and convolution":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "n fold integer programming via lp rounding")
  Member "scheduling meets n fold integer programming":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "n fold integer programming via lp rounding")
  Member "the complexity landscape of decompositional parameters for ilp":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "parameterized algorithms for milps with small treedepth")
  Member "evaluating and tuning n fold integer programming":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "near linear time algorithm for n fold ilps via color coding")
  Member "combinatorial n fold integer programming and applications":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "n fold integer programming via lp rounding")

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)