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 "nearly optimal np hardness of vertex cover on k uniform k partite hypergraphs"):
  Abstract: We study the problem of computing the minimum vertex cover on k-uniform k-partite hypergraphs when the k-partition is given. On bipartite graphs (k = 2), the minimum vertex cover can be computed in polynomial time. For general k, the problem was studied by Lov\'asz, who gave a k/2 -approximation based on the standard LP relaxation. Subsequent work by Aharoni, Holzman and Krivelevich showed a tight integrality gap of (k/2 - o(1)) for the LP relaxation. While this problem was known to be NP-hard for k >= 3, the first non-trivial NP-hardness of approximation factor of k/4- \eps was shown in a recent work by Guruswami and Saket. They also showed that assuming Khot's Unique Games Conjecture yields a k/2 - \eps inapproximability for this problem, implying the optimality of Lov\'asz's result. #R##N#In this work, we show that this problem is NP-hard to approximate within k/2- 1 + 1/2k -\eps. This hardness factor is off from the optimal by an additive constant of at most 1 for k >= 4. Our reduction relies on the Multi-Layered PCP of Dinur et al. and uses a gadget - based on biased Long Codes - adapted from the LP integrality gap of Aharoni et al. The nature of our reduction requires the analysis of several Long Codes with different biases, for which we prove structural properties of the so called cross-intersecting collections of set families - variants of which have been studied in extremal set theory.

Includes members:
  Member "on the optimality of a class of lp based algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "optimal constant time approximation algorithms and unconditional inapproximability results for every bounded degree csp")
  Member "a new multilayered pcp and the hardness of hypergraph vertex cover":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "an improved algorithm for dynamic set cover")

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.CC(Computational Complexity)