Subquadratic 3SUM and Subcubic APSP

Researchers have made significant breakthroughs in two important problems in computer science: the 3SUM problem and the All Pairs Shortest Paths (APSP) problem. The 3SUM problem, which involves determining whether three numbers in an array sum up to zero, has been solved in subquadratic time. This achievement is notable as it has been an open problem for over 20 years. Additionally, the researchers have also made progress on the APSP problem, which involves finding the shortest paths between all pairs of vertices in a weighted graph. They have achieved a subcubic time complexity for this problem, improving upon the previous best known algorithm. These breakthroughs have important implications for many areas of computer science, including algorithms, graph theory, and computational complexity theory.