The secondary school teaching supervision system is a beneficial supplement of establishing school-level teaching supervision system, and it also is an important means of promoting the steady improvement of teaching quality in schools and universities. The object of this dissertation is the secondary school teaching supervision system and the aim of this dissertation is to transfer the relationship between “supervision” and “guidance”, so the secondary teaching supervision system which mainly based on the stimulation, takes guidance as the major and uses supervision as the supplement is proposed. Based on this system, the dissertation gives the specific execution strategy about the construction of supervision team, the innovation of supervision content and the cultivation of supervisor, etc. Finally, the dissertation analyzed the advantages of this secondary school teaching supervision system.

Given the scheduling model of bike-sharing, we consider the problem of hitting a set of n axis-parallel line segments in \(\mathbb {R}^2\) by a square or an \(\ell _\infty \)-circle (and two squares, or two \(\ell _\infty \)-circles) whose center(s) must lie on some line segment(s) such that the (maximum) edge length of the square(s) is minimized. Under a different tree model, we consider (virtual) hitting circles whose centers must lie on some tree edges with similar minmax-objectives (with the distance between a center to a target segment being the shortest path length between them). To be more specific, we consider the cases when one needs to compute one (and two) centers on some edge(s) of a tree with m edges, where n target segments must be hit, and the objective is to minimize the maximum path length from the target segments to the nearer center(s). We give three linear-time algorithms and an \(O(n^2\log n)\) algorithm for the four problems in consideration.

We consider a variant of visibility-constrained Voronoi diagrams for n given point sites in the Euclidean plane. Whereas such diagrams typically are of size Ω(n2), the combinatorial and algorithmic complexity of the studied variant is significantly subquadratic in n.

Minimum Common String Partition (MCSP) has drawn a lot of attention due to its application in genome rearrangement. The best approximation algorithm has a factor O(lognlog* n) and it was shown most recently that it is FPT (but with a very high running time). In this paper, we consider the decision version of the one-sided MCSP problem (formally called the exact block cover problem); namely, when one sequence is already partitioned into k blocks, how to decide whether the other sequence can be partitioned accordingly. While this decision problem is obviously in FPT, we show interesting results in this paper: (1) If each letter is allowed to appear at most twice (or three times), then the problem is polynomially solvable, (2) There is an FPT algorithm which runs in O *(2 k ) time, improving the trivial bound of O *(k!), and (3) If |Σ| = c, c being a constant at least 2, then the problem is NP-complete.