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 "toward a dichotomy for approximation of h coloring"):
  Abstract: Given two (di)graphs G, H and a cost function $c:V(G)\times V(H) \to \mathbb{Q}_{\geq 0}\cup\{+\infty\}$, in the minimum cost homomorphism problem, MinHOM(H), goal is finding a homomorphism $f:V(G)\to V(H)$ (a.k.a H-coloring) that minimizes $\sum\limits_{v\in V(G)}c(v,f(v))$. The complexity of exact minimization of this problem is well understood [34], and the class of digraphs H, for which the MinHOM(H) is polynomial time solvable is a small subset of all digraphs. #R##N#In this paper, we consider the approximation of MinHOM within a constant factor. For digraphs, MinHOM(H) is not approximable if H contains a digraph asteroidal triple (DAT). We take a major step toward a dichotomy classification of approximable cases. We give a dichotomy classification for approximating the MinHOM(H) when H is a graph. For digraphs, we provide constant factor approximation algorithms for two important classes of digraphs, namely bi-arc digraphs (digraphs with a conservative semi-lattice polymorphism or min-ordering), and k-arc digraphs (digraphs with an extended min-ordering). Specifically, we show that: #R##N#1. \textbf{Dichotomy for Graphs:} MinHOM(H) has a $2|V(H)|$-approximation algorithm if graph H admits a conservative majority polymorphims (i.e. H is a bi-arc graph), otherwise, it is inapproximable; #R##N#2. MinHOM(H) has a $|V(H)|^2$-approximation algorithm if H is a bi-arc digraph; #R##N#3. MinHOM(H) has a $|V(H)|^2$-approximation algorithm if H is a k-arc digraph. #R##N#In conclusion, we show the importance of these results and provide insights for achieving a dichotomy classification of approximable cases. Our constant factors depend on the size of H. However, the implementation of our algorithms provides a much better approximation ratio. It leaves open to investigate a classification of digraphs H, where MinHOM(H) admits a constant factor approximation algorithm that is independent of H.

Includes members:
  Member "interval like graphs and digraphs":
    also connected through other hyperedges:
      (none)
  Member "binarisation for valued constraint satisfaction problems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the power of sherali adams relaxations for general valued csps")
  Member "towards a characterization of constant factor approximable finite valued csps":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "algebraic approach to promise constraint satisfaction")
  Member "bi arc digraphs and conservative polymorphisms":
    also connected through other hyperedges:
      (none)
  Member "the complexity of general valued csps":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the complexity of boolean surjective general valued csps")
  Member "local distribution and the symmetry gap approximability of multiway partitioning problems":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "optimizing item and subgroup configurations for social aware vr shopping")
  Member "conservative constraint satisfaction re revisited":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "hardness of network satisfaction for relation algebras with normal representations")
  Member "computational complexity of the minimum cost homomorphism problem on three element domains":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "binarisation for valued constraint satisfaction problems")

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)