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 "integrality gaps for strengthened lp relaxations of capacitated and lower bounded facility location"):
  Abstract: The metric uncapacitated facility location problem (UFL) enjoys a special stature in approximation algorithms as a testbed for various techniques. Two generalizations of UFL are capacitated facility location (CFL) and lower-bounded facility location (LBFL). In the former, every facility has a capacity which is the maximum demand that can be assigned to it, while in the latter, every open facility is required to serve a given minimum amount of demand. Both CFL and LBFL are approximable within a constant factor but their respective natural LP relaxations have an unbounded integrality gap. According to Shmoys and Williamson, the existence of a relaxation-based algorithm for CFL is one of the top 10 open problems in approximation algorithms. #R##N#In this paper we give the first results on this problem. We provide substantial evidence against the existence of a good LP relaxation for CFL by showing unbounded integrality gaps for two families of strengthened formulations. #R##N#The first family we consider is the hierarchy of LPs resulting from repeated applications of the lift-and-project Lov\'{a}sz-Schrijver procedure starting from the standard relaxation. We show that the LP relaxation for CFL resulting after $\Omega(n)$ rounds, where $n$ is the number of facilities in the instance, has unbounded integrality gap. Note that the Lov\'{a}sz-Schrijver procedure is known to yield an exact formulation for CFL in at most $n$ rounds. #R##N#We also introduce the family of proper relaxations which generalizes to its logical extreme the classic star relaxation, an equivalent form of the natural LP. We characterize the integrality gap of proper relaxations for both LBFL and CFL and show a threshold phenomenon under which it decreases from unbounded to 1.

Includes members:
  Member "approximating k median via pseudo approximation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "fair correlation clustering")
  Member "approximation limits of linear programs beyond hierarchies":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "compressing permutation groups into grammars and polytopes a graph embedding approach")
  Member "lp rounding for k centers with non uniform hard capacities":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "fair clustering with multiple colors")
  Member "improved approximation guarantees for lower bounded facility location":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "fair algorithms for clustering")
  Member "polynomial integrality gaps for strong sdp relaxations of densest k subgraph":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "high dimensional estimation via sum of squares proofs")
  Member "santa claus schedules jobs on unrelated machines":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "weighted completion time minimization for unrelated machines via iterative fair contention resolution")
  Member "new constructive aspects of the lovasz local lemma":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "fast sampling and counting k sat solutions in the local lemma regime")
  Member "greedy facility location algorithms analyzed using dual fitting with factor revealing lp":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "cache optimization models and algorithms")

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)