The shortest path counting is an important research problem in graph computing. It aims to query the number of shortest paths between vertices， which is widely used in path planning and recommendation， social network analysis， betweenness centrality calculation and so on. At present， more and more networks can be modeled as temporal graphs， but there is no research work on the shortest path counting query problem of temporal graphs. Compared with the static graph， the temporal graph increases the time information， the structure is more complex， and the activation time of the edge must be considered when querying the number of paths between vertices. Therefore， the shortest path counting method for the static graphs is no longer applicable to the temporal graphs， and querying on large-scale temporal graphs is more challenging. In order to solve the shortest path counting problem of temporal graphs， a method of TG-TL （Temporal Graph-Tree Label） index based on tree decomposition was proposed. The method consists of two stages： index construction and online query. In the index construction stage， the temporal tree decomposition algorithm was designed according to the attributes of the temporal graph， and the temporal graph was transformed into a tree structure. Then， according to the structure information of tree decomposition and convex path definition， an efficient index building algorithm was proposed. In the online query stage， an efficient temporal shortest path counting query algorithm was proposed based on TG-TL index. Experiments were carried out on 4 real datasets， and the experimental results showed that compared with the query algorithm based on TG-base （Temporal Graph-base） index， the proposed algorithm improved the query efficiency by 61% at least. Therefore， the proposed algorithm is efficient and effective for the shortest path counting problem of temporal graphs.

In order to improve chaos complexity and provide more reliable chaotic system for image encryption, and enhance the security of image encryption algorithm, a new image encryption algorithm based on two-dimensional inverse-trigonometric hyperchaotic system was proposed. Firstly, based on one-dimensional triangular function, a two-dimensional inverse-trigonometric hyperchaotic system was constructed. Compared with some two-dimensional chaotic systems, this system had wider chaotic range, more random iteration sequences and better ergodicity by simulation experiments about bifurcation diagram and Lyapunov exponent. Then based on the proposed chaotic system, the "scrambling-diffusion" strategy was designed and different keys were given, which were used to generate different hyperchaotic sequences. The image matrix was scrambled without repetition by hyperchaotic sequences, then the scrambled sequence were shifted and diffused. So the ciphertext was obtained by looping thrice. Finally, histogram analysis, key space analysis, correlation analysis of adjacent pixels, plaintext sensitivity analysis and information entropy analysis were carried out. The test values of Number of Pixels Change Rate (NPCR) and Unified Average Changing Intersity (UACI) of ciphertext images were very close to their ideal expected values. The test results of information entropy were about 7.997, which was also very close to the expected value of 8. The experimental results show that the image encryption system has more reliable security, stronger ability to resist attacks, and had a good application prospect in the field of image security.

The method for iterative probability relaxation segmentation used in cell division can overcome the difficult issues on account of complicated cellular structure and phenomenon of serious adhesion, while the general segmentation algorithm cannot make it effectively. In addition, because of tense embedded resources under the environment of Linux system, the iterative relaxation cellular segmentation algorithm has been improved and then added to the embedded cellular segmentation system based on Qt and OpenCV. The experimental results demonstrate that the improved algorithm can effectively solve the difficult problem of cell division efficaciously and the naked eye can clearly distinguish the difference between the nucleus, cytoplasm and glands. The improved algorithm increases the processing speed and can be transplanted to the embedded facilities convenient for carrying, diagnosing and treating.