{"paper":{"title":"Revisiting Sparse Matrix Coloring and Bicoloring","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","cs.MS","cs.NA","math.CO"],"primary_cat":"math.NA","authors_text":"Alexis Montoison, Assefaw Gebremedhin, Guillaume Dalle","submitted_at":"2025-05-12T07:54:06Z","abstract_excerpt":"Sparse matrix coloring and bicoloring are fundamental building blocks of sparse automatic differentiation. Bicoloring is particularly advantageous for rectangular Jacobian matrices with at least one dense row and column. Indeed, in such cases, unidirectional row or column coloring demands a number of colors equal to the number of rows or columns. We introduce a new strategy for bicoloring that encompasses both direct and substitution-based decompression approaches. Our method reformulates the two variants of bicoloring as star and acyclic colorings of an augmented symmetric matrix. We extend t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07308","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.07308/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}