The field of geometric algorithms is experiencing significant advancements, driven by innovative techniques and optimization methods. Recent developments focus on improving the efficiency and accuracy of algorithms for various geometric problems, such as curve separation, facility assignment, and graph optimization. A notable trend is the use of primal-dual methods, which have been successfully applied to edge-covering problems, yielding improved approximation ratios. Additionally, researchers are exploring new approaches to automate the search for small hard examples, which can help identify weaknesses in approximation algorithms. The development of faster algorithms for reverse shortest path problems and geometric optimization tasks is also a key area of research. Noteworthy papers include:

• The study on finding a shortest curve that separates few objects from many, which presents a fixed-parameter tractable algorithm.
• The work on tight analysis of the primal-dual method for edge-covering pliable set families, which improves the approximation ratio.
• The research on automating the search for small hard examples to approximation algorithms, which develops a technique for constructing decision trees and running linear programs.