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 "bi factor approximation algorithms for hard capacitated k median problems"):
  Abstract: The $k$-Facility Location problem is a generalization of the classical problems $k$-Median and Facility Location. The goal is to select a subset of at most $k$ facilities that minimizes the total cost of opened facilities and established connections between clients and opened facilities. We consider the hard-capacitated version of the problem, where a single facility may only serve a limited number of clients and creating multiple copies of a facility is not allowed. We construct approximation algorithms slightly violating the capacities based on rounding a fractional solution to the standard LP. #R##N#It is well known that the standard LP (even in the case of uniform capacities and opening costs) has unbounded integrality gap if we only allow violating capacities by a factor smaller than $2$, or if we only allow violating the number of facilities by a factor smaller than $2$. In this paper, we present the first constant-factor approximation algorithms for the hard-capacitated variants of the problem. For uniform capacities, we obtain a $(2+\varepsilon)$-capacity violating algorithm with approximation ratio $O(1/\varepsilon^2)$; our result has not yet been improved. Then, for non-uniform capacities, we consider the case of $k$-Median, which is equivalent to $k$-Facility Location with uniform opening cost of the facilities. Here, we obtain a $(3+\varepsilon)$-capacity violating algorithm with approximation ratio $O(1/\varepsilon)$.

Includes members:
  Member "an improved approximation algorithm for the hard uniform capacitated k median problem":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "improved local search based approximation algorithm for hard uniform capacitated k median problem")
  Member "on uniform capacitated k median beyond the natural lp relaxation":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "fair clustering with multiple colors")
  Member "an improved approximation for k median and positive correlation in budgeted optimization":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "individual fairness for k clustering")
  Member "lp based algorithms for capacitated facility location":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "easy capacitated facility location problems with connections to lot sizing")
  Member "approximation algorithms for hard capacitated k facility location problems":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "facility location problem with capacity constraints algorithmic and mechanism design perspectives")
  Member "approximating k median via pseudo approximation":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "fair correlation clustering")
  Member "lp rounding for k centers with non uniform hard capacities":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "fair clustering with multiple colors")
  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)