Multiset resolvability parameters in graphs: A survey with new results and open problems

What the math gives to ML

The paper's central transferable object is a permutation-invariant distance signature: instead of retaining ordered distances from a landmark set, represent a vertex by the multiset, or histogram, of its distances to those landmarks. This provides a principled positional encoding for graph neural networks that is invariant to arbitrary landmark ordering and can distinguish nodes even when ordinary pooled features collide. The graph-theoretic lower bounds also suggest data-dependent landmark budgets, especially for diameter-two or highly symmetric graphs, where many anchors are provably necessary. The most practical transfer is a sparse multiset-distance positional encoding combined with collision-aware landmark selection.