Tootfinder

Bootstrap Learning for Combinatorial Graph Alignment with Sequential GNNs
Marc Lelarge
https://arxiv.org/abs/2510.03086 https://arxiv.org/pdf/2510.03086

Bootstrap Learning for Combinatorial Graph Alignment with Sequential GNNs
Graph neural networks (GNNs) have struggled to outperform traditional optimization methods on combinatorial problems, limiting their practical impact. We address this gap by introducing a novel chaining procedure for the graph alignment problem, a fundamental NP-hard task of finding optimal node correspondences between unlabeled graphs using only structural information. Our method trains a sequence of GNNs where each network learns to iteratively refine similarity matrices produced by previous …

Three-Neighbour Bootstrap Percolation in Thin Three-Dimensional Grids
Will Dolphin, Peter J. Dukes
https://arxiv.org/abs/2509.13589 https://arxiv.org/pdf/2…

Three-Neighbour Bootstrap Percolation in Thin Three-Dimensional Grids
We improve the status of the problem of determining minimum-sized percolating sets in $a \times b \times c$ grids under the $3$-neighbour process. Using several new constructions, we show that optimal percolating sets exist whenever $\min(a,b,c) \ge 7$. As an important step toward this, we also show that all grids with $\min(a,b,c) \ge 4$ have a percolating set whose size exactly achieves the lower bound $(ab+ac+bc)/3$ whenever this value is an integer.