The field of graph partitioning and streaming algorithms is witnessing significant developments, with a focus on improving approximation bounds and understanding the limitations of streaming models. Researchers are exploring new techniques to overcome the challenges posed by large-scale graph data, including the development of novel lower bounds and approximation algorithms. A key direction of research is the investigation of multi-pass streaming algorithms, which has led to a better understanding of the trade-offs between pass complexity and space requirements. Additionally, there is a growing interest in vertex partitioning methods, which aim to bound the cutwidth of graphs by partitioning their vertices. Noteworthy papers in this area include:

• A paper that improves upon the state-of-the-art result for multi-pass streaming lower bounds for approximating Max-Cut, showing that any non-trivial approximation algorithm requires either polynomially many passes or polynomially large space.
• A paper that studies the cutwidth measure on graphs and provides bounds expressed as a function of the maximal cutwidth of subgraphs induced by partition classes and the cutwidth of the quotient multigraph.
• A paper that investigates edge-weighted balanced connected partitions and shows that both the min-max and max-min versions of the problem are NP-hard on various graph classes.