The recent developments in the research area have significantly advanced the understanding and efficiency of several classic combinatorial problems. Notably, there has been a surge in the application of geometric interpretations and algorithmic innovations to tackle problems such as the Subset Sum Problem (SSP) and the Capacitated $d$-Hitting Set. These advancements have led to the development of Fully Polynomial-Time Approximation Schemes (FPTAS) and parameterized approximation algorithms, which not only improve upon existing methods but also provide new insights into the complexity of these problems. Additionally, there has been a focus on revisiting and improving upon foundational algorithms like Bellman's algorithm for Subset Sum, with novel approaches leveraging results from additive combinatorics to achieve superior performance across all parameter regimes. The study of Constraint Satisfaction Problems (CSPs) has also seen significant contributions, particularly in the context of complete instances and the decision versions of CSPs, which have been shown to admit quasi-polynomial time algorithms. Furthermore, the problem of approximately counting Knapsack solutions has been addressed with a subquadratic time algorithm, breaking through a previously perceived barrier in the field. These developments collectively indicate a shift towards more efficient and versatile algorithms, with a strong emphasis on both theoretical advancements and practical implications.