The field of combinatorial modeling and algorithmic techniques is witnessing significant developments, with a focus on capturing higher-order dependencies and complex relationships in large data sets. Researchers are introducing new combinatorial models and algorithms to analyze and reconstruct complex phenomena, such as sets of strings from their k-way projections. Additionally, there is a growing interest in constrained clustering problems, including connected clustering, which has applications in community detection and geodesy. Furthermore, advancements in phylogenetic networks and tree containment problems are being made, with a focus on robustness to uncertainty and poorly supported branches in biological data. Noteworthy papers in this area include:

• A paper that introduces a new algorithm for reconstructing sets of strings from their k-way projections, using a modified version of overlap graphs from genetic reconstruction algorithms.
• A paper that provides hardness results and approximation algorithms for connected clustering problems, including an Omega(log*(k))-hardness result for connected k-center and a (3 + epsilon)-approximation algorithm for connected min-sum-radii.
• A paper that presents an algorithm for solving Soft Tree Containment in phylogenetic networks, leveraging the fact that networks often exhibit low scanwidth, making the problem more tractable.