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 "tight complexity lower bounds for integer linear programming with few constraints"):
  Abstract: We consider the ILP Feasibility problem: given an integer linear program $\{Ax = b, x\geq 0\}$, where $A$ is an integer matrix with $k$ rows and $\ell$ columns and $b$ is a vector of $k$ integers, we ask whether there exists $x\in\mathbb{N}^\ell$ that satisfies $Ax = b$. Our goal is to study the complexity of ILP Feasibility when both $k$, the number of constraints (rows of $A$), and $\|A\|_\infty$, the largest absolute value in $A$, are small. #R##N#Papadimitriou [J. ACM, 1981] was the first to give a fixed-parameter algorithm for ILP Feasibility in this setting, with running time $\left((\|A\mid b\|_\infty) \cdot k\right)^{O(k^2)}$. This was very recently improved by Eisenbrand and Weismantel [SODA 2018], who used the Steinitz lemma to design an algorithm with running time $(k\|A\|_\infty)^{O(k)}\cdot \|b\|_\infty^2$, and subsequently by Jansen and Rohwedder [2018] to $O(k\|A\|_\infty)^{k}\cdot \log \|b\|_\infty$. We prove that for $\{0,1\}$-matrices $A$, the dependency on $k$ is probably optimal: an algorithm with running time $2^{o(k\log k)}\cdot (\ell+\|b\|_\infty)^{o(k)}$ would contradict ETH. This improves previous non-tight lower bounds of Fomin et al. [ESA 2018]. #R##N#We then consider ILPs with many constraints, but structured in a shallow way. Precisely, we consider the dual treedepth of the matrix $A$, which is the treedepth of the graph over the rows of $A$, with two rows adjacent if in some column they both contain a non-zero entry. It was recently shown by Kouteck\'{y} et al. [ICALP 2018] that ILP Feasibility can be solved in time $\|A\|_\infty^{2^{O(td(A))}}\cdot (k+\ell+\log \|b\|_\infty)^{O(1)}$. We present a streamlined proof of this fact and prove optimality: even assuming that all entries of $A$ and $b$ are in $\{-1,0,1\}$, the existence of an algorithm with running time $2^{2^{o(td(A))}}\cdot (k+\ell)^{O(1)}$ would contradict ETH.

Includes members:
  Member "a row invariant parameterized algorithm for integer programming":
    also connected through other hyperedges:
      (none)
  Member "about the complexity of two stage stochastic ips":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "fuzzy simultaneous congruences")
  Member "scheduling meets n fold integer programming":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "n fold integer programming via lp rounding")
  Member "seth based lower bounds for subset sum and bicriteria path":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "scheduling lower bounds via and subset sum")
  Member "proximity results and faster algorithms for integer programming using the steinitz lemma":
    also connected through other hyperedges:
      - Hyperedge HE-4 (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)