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 "on the tree augmentation problem"):
  Abstract: In the Tree Augmentation problem we are given a tree $T=(V,F)$ and a set $E \subseteq V \times V$ of edges with positive integer costs $\{c_e:e \in E\}$. The goal is to augment $T$ by a minimum cost edge set $J \subseteq E$ such that $T \cup J$ is $2$-edge-connected. We obtain the following results. #R##N#Recently, Adjiashvili [SODA 17] introduced a novel LP for the problem and used it to break the $2$-approximation barrier for instances when the maximum cost $M$ of an edge in $E$ is bounded by a constant; his algorithm computes a $1.96418+\epsilon$ approximate solution in time $n^{{(M/\epsilon^2)}^{O(1)}}$. Using a simpler LP, we achieve ratio $\frac{12}{7}+\epsilon$ in time $2^{O(M/\epsilon^2)} poly(n)$.This gives ratio better than $2$ for logarithmic costs, and not only for constant costs. #R##N#One of the oldest open questions for the problem is whether for unit costs (when $M=1$) the standard LP-relaxation, so called Cut-LP, has integrality gap less than $2$. We resolve this open question by proving that for unit costs the integrality gap of the Cut-LP is at most $28/15=2-2/15$. In addition, we will prove that another natural LP-relaxation, that is much simpler than the ones in previous work, has integrality gap at most $7/4$.

Includes members:
  Member "improved approximation for tree augmentation saving by rewiring":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "2 node connectivity network design")
  Member "a simplified 1 5 approximation algorithm for augmenting edge connectivity of a graph from 1 to 2":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "2 node connectivity network design")
  Member "approximating unweighted tree augmentation via lift and project part ii":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "breaching the 2 approximation barrier for connectivity augmentation a reduction to steiner tree")
  Member "fixed parameter algorithms for minimum cost edge connectivity augmentation":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "minimum weight connectivity augmentation for planar straight line graphs")

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)