A novel approach for calculating single-source shortest paths of weighted digraphs based on rough sets theory.

Calculating single-source shortest paths (SSSPs) rapidly and precisely from weighted digraphs is a crucial problem in graph theory. As a mathematical model of processing uncertain tasks, rough sets theory (RST) has been proven to possess the ability of investigating graph theory problems. Recently, some efficient RST approaches for discovering different subgraphs (e.g. strongly connected components) have been presented. This work was devoted to discovering SSSPs of weighted digraphs by aid of RST. First, SSSPs problem was probed by RST, which aimed at supporting the fundamental theory for taking RST approach to calculate SSSPs from weighted digraphs. Second, a heuristic search strategy was designed. The weights of edges can be served as heuristic information to optimize the search way of $ k $-step $ R $-related set, which is an RST operator. By using heuristic search strategy, some invalid searches can be avoided, thereby the efficiency of discovering SSSPs was promoted. Finally, the W3SP@R algorithm based on RST was presented to calculate SSSPs of weighted digraphs. Related experiments were implemented to verify the W3SP@R algorithm. The result exhibited that W3SP@R can precisely calculate SSSPs with competitive efficiency.

Element detection and segmentation of mathematical function graphs based on improved Mask R-CNN.

There are approximately 2.2 billion people around the world with varying degrees of visual impairments. Among them, individuals with severe visual impairments predominantly rely on hearing and touch to gather external information. At present, there are limited reading materials for the visually impaired, mostly in the form of audio or text, which cannot satisfy the needs for the visually impaired to comprehend graphical content. Although many scholars have devoted their efforts to investigating methods for converting visual images into tactile graphics, tactile graphic translation fails to meet the reading needs of visually impaired individuals due to image type diversity and limitations in image recognition technology. The primary goal of this paper is to enable the visually impaired to gain a greater understanding of the natural sciences by transforming images of mathematical functions into an electronic format for the production of tactile graphics. In an effort to enhance the accuracy and efficiency of graph element recognition and segmentation of function graphs, this paper proposes an MA Mask R-CNN model which utilizes MA ConvNeXt as its improved feature extraction backbone network and MA BiFPN as its improved feature fusion network. The MA ConvNeXt is a novel feature extraction network proposed in this paper, while the MA BiFPN is a novel feature fusion network introduced in this paper. This model combines the information of local relations, global relations and different channels to form an attention mechanism that is able to establish multiple connections, thus increasing the detection capability of the original Mask R-CNN model on slender and multi-type targets by combining a variety of multi-scale features. Finally, the experimental results show that MA Mask R-CNN attains an 89.6% mAP value for target detection and 72.3% mAP value for target segmentation in the instance segmentation of function graphs. This results in a 9% mAP improvement for target detection and 12.8% mAP improvement for target segmentation compared to the original Mask R-CNN.