Adaptive Graph Pebbling for Localized Graph-Laplacian Regularization

This preprint presents an adaptive graph-pebbling approach to localized graph-Laplacian regularization. It investigates boundary-aware localization and compares pebble-selection strategies based on graph disagreement, random sampling, and spatial coverage on a synthetic 3D Gaussian graph. Preliminary experiments using a controlled quadratic surrogate objective suggest that combining high-disagreement candidate selection with farthest-point spatial sampling can improve objective values under limited computation budgets. End-to-end reconstruction improvements have not yet been established.