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 "box covers and domain orderings for beyond worst case join processing"):
  Abstract: Recent beyond worst-case optimal join algorithms Minesweeper and its generalization Tetris have brought the theory of indexing and join processing together by developing a geometric framework for joins. These algorithms take as input an index $\mathcal{B}$, referred to as a box cover, that stores output gaps that can be inferred from traditional indexes, such as B+ trees or tries, on the input relations. The performances of these algorithms highly depend on the certificate of $\mathcal{B}$, which is the smallest subset of gaps in $\mathcal{B}$ whose union covers all of the gaps in the output space of a query $Q$. Different box covers can have different size certificates and the sizes of both the box covers and certificates highly depend on the ordering of the domain values of the attributes in $Q$. We study how to generate box covers that contain small size certificates to guarantee efficient runtimes for these algorithms. First, given a query $Q$ over a set of relations of size $N$ and a fixed set of domain orderings for the attributes, we give a $\tilde{O}(N)$-time algorithm that generates a box cover for $Q$ that is guaranteed to contain the smallest size certificate across any box cover for $Q$. Second, we show that finding a domain ordering to minimize the box cover size and certificate is NP-hard through a reduction from the 2 consecutive block minimization problem on boolean matrices. Our third contribution is an $\tilde{O}(N)$-time approximation algorithm to compute domain orderings, under which one can compute a box cover of size $\tilde{O}(K^r)$, where $K$ is the minimum box cover for $Q$ under any domain ordering and $r$ is the maximum arity of any relation. This guarantees certificates of size $\tilde{O}(K^r)$. Our results provide several new beyond worst-case bounds, which on some inputs and queries can be unboundedly better than the bounds stated in prior work.

Includes members:
  Member "worst case optimal join algorithms techniques results and open problems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "rk means fast clustering for relational data")
  Member "size bounds and query plans for relational joins":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "complexity analysis of general and fractional hypertree decompositions")
  Member "constraint solving via fractional edge covers":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "complexity analysis of general and fractional hypertree decompositions")
  Member "computing join queries with functional dependencies":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "bag query containment and information theory")
  Member "it s all a matter of degree using degree information to optimize multiway joins":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "instance and output optimal parallel algorithms for acyclic joins")
  Member "joins via geometric resolutions worst case and beyond":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "complexity analysis of general and fractional hypertree decompositions")
  Member "beyond worst case analysis for joins with minesweeper":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "instance and output optimal parallel algorithms for acyclic joins")
  Member "worst case optimal join algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "fast join project query evaluation using matrix multiplication")

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.DB(Databases)