The Minimum Dominating Set (MDS) problem is a well-established combinatorial optimization problem with numerous real-world applications. Its NP-hard nature makes it increasingly difficult to obtain exact solutions as the graph size grows. This paper introduces ParDS, an exact algorithm developed to address the MDS problem within the branch-and-bound framework. ParDS features two key innovations: an advanced linear programming technique that yields tighter lower bounds and a set of novel reduction rules that dynamically simplify instances throughout the solving process. Compared to the leading exact algorithms presented at IJCAI 2023 and 2024, ParDS demonstrates theoretically superior lower-bound quality. Experimental results on standard benchmark datasets highlight several significant advantages of ParDS: it achieves fastest solving times in 70% of graph categories, especially on large, sparse graphs, delivers a speed-up of up to 3,411 times on the fastest individual instance, and successfully solves 16 out of 43 instances that other algorithms were unable to resolve within the 5-hour time limit. These findings establish ParDS as a state-of-the-art solution for exactly solving the MDS problem

Traditional photography composition approaches are dominated by 2D cropping-based methods. However, these methods fall short when scenes contain poorly arranged subjects. Professional photographers often employ perspective adjustment as a form of 3D recomposition, modifying the projected 2D relationships between subjects while maintaining their actual spatial positions to achieve better compositional balance. Inspired by this artistic practice, we propose photography perspective composition (PPC), extending beyond traditional cropping-based methods. However, implementing the PPC faces significant challenges: the scarcity of perspective transformation datasets and undefined assessment criteria for perspective quality. To address these challenges, we present three key contributions: (1) An automated framework for building PPC datasets through expert photographs. (2) A video generation approach that demonstrates the transformation process from less favorable to aesthetically enhanced perspectives. (3) A perspective quality assessment (PQA) model constructed based on human performance. Our approach is concise and requires no additional prompt instructions or camera trajectories, helping and guiding ordinary users to enhance their composition skills.