TL;DR
A preliminary comparison with the A ∗ -based algorithms indicates that they are outperformed by the ILP-based approaches on graphs exceeding ten nodes, and a dataset of optimal edit paths across widely used datasets from the TUDataset is released.
This work proposes to amortize the graph matching (node alignment) problem and showcases the efficiency of this approach on toy and real world SGP problems of increasing complexity including a novel Mass-spectra to Scaffold task that is introduced.
It is shown that bidirectional Dijkstra is still instance-optimal on simple undirected weighted graphs under the order-oblivious model, where incident edges are given in a random order, and under the order-dependent model, where bidirectional Dijkstra is not instance-optimal.
A novel dataset of 70 underexplored graph construction problems that require finding Ramsey-good graphs with special properties, which shows that LLMs achieve only 37.70% accuracy on the hard-tier problems in this dataset, with Gemma-4-31B achieving the highest performance out of the five.
The Dual-GNN Multilevel Coarsening framework uses learning to guide multilevel graph coarsening while retaining combinatorial search for final decision making and achieves the best mean solution quality among all evaluated methods.
An automatic pipeline that is problem-agnostic to all problems in the MiniZinc format is built, finding that algorithm selection achieves a 39.6% average problem-weighted win rate against a one-shot Gurobi baseline, more than doubling the best single configuration (19.3%).
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