We study the skeleton of several polytopes related to the n-cube, the halved n-cube, and the folded n-cube. In particular, the Gale polytope of the n-cube, its dual and the duals of the halved n-cube and the complete bipartite sub-graphs polytope.

We revisit the Raz-Safra plane-vs.-plane test and study the closely related cube vs. cube test. In this test the tester has access to a “cubes table” which assigns to every cube a low degree polynomial. The tester randomly selects two cubes (affine sub-spaces of dimension 3) that intersect on a point x ∈ F, and checks that the assignments to the cubes agree with each other on the point x. Our m...

Data cube construction is a commonly used operation in data warehouses. Because of the volume of data stored and analyzed in a data warehouse and the amount of computation involved in data cube construction, incremental maintenance of data cube is really effective. To maintain a data cube incrementally, previous methods were mainly for relational databases. In this paper, we employ an extendibl...