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 "maximum size envy free matchings"):
  Abstract: We consider the problem of assigning residents to hospitals when hospitals have upper and lower quotas. Apart from this, both residents and hospitals have a preference list which is a strict ordering on a subset of the other side. Stability is a well-known notion of optimality in this setting. #R##N#Every Hospital-Residents (HR) instance without lower quotas admits at least one stable matching. When hospitals have lower quotas (HRLQ), there exist instances for which no matching that is simultaneously stable and feasible exists. We investigate envy-freeness which is a relaxation of stability for such instances. Yokoi (ISAAC 2017) gave a characterization for HRLQ instances that admit a feasible and envy-free matching. Yokoi's algorithm gives a minimum size feasible envy-free matching, if there exists one. We investigate the complexity of computing a maximum size envy-free matching in an HRLQ instance (MAXEFM problem) which is equivalent to computing an envy-free matching with minimum number of unmatched residents (MIN-UR-EFM problem). #R##N#We show that both the MAXEFM and MIN-UR-EFM problems for an HRLQ instance with arbitrary incomplete preference lists are NP-hard. We show that MAXEFM cannot be approximated within a factor of 21/19. On the other hand we show that the MIN-UR-EFM problem cannot be approximated for any alpha > 0. We present 1/(L+1) approximation algorithm for MAXEFM when quotas are at most 1 where L is the length of longest preference list of a resident. We also show that both the problems become tractable with additional restrictions on preference lists and quotas. We also investigate the parameterized complexity of these problems and prove that they are W[1]-hard when deficiency is the parameter. On the positive side, we show that the problems are fixed parameter tractable for several interesting parameters.

Includes members:
  Member "envy free matchings with lower quotas":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "how good are popular matchings")
  Member "popular matching with lower quotas":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "how good are popular matchings")

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)