Cut Problem

The Max-Cut problem, a fundamental NP-hard combinatorial optimization challenge, seeks to partition a graph's nodes into two sets to maximize the number of edges connecting nodes in different sets. Current research focuses on developing efficient algorithms, including those leveraging graph neural networks (GNNs) and incorporating heuristics to improve approximation quality and scalability, particularly for large graphs and those with constraints. These advancements are crucial for various applications, such as graph clustering, image summarization, and solving problems in physics and engineering, where finding near-optimal solutions within reasonable timeframes is essential. Benchmarking efforts are underway to standardize evaluation and compare the performance of different approaches.