{"paper":{"title":"Efficient algorithms for computing a minimal homology basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.CO"],"primary_cat":"math.AT","authors_text":"Tamal K. Dey, Tianqi Li, Yusu Wang","submitted_at":"2018-01-21T03:37:26Z","abstract_excerpt":"Efficient computation of shortest cycles which form a homology basis under $\\mathbb{Z}_2$-additions in a given simplicial complex $\\mathcal{K}$ has been researched actively in recent years. When the complex $\\mathcal{K}$ is a weighted graph with $n$ vertices and $m$ edges, the problem of computing a shortest (homology) cycle basis is known to be solvable in $O(m^2n/\\log n+ n^2m)$-time. Several works \\cite{borradaile2017minimum, greedy} have addressed the case when the complex $\\mathcal{K}$ is a $2$-manifold. The complexity of these algorithms depends on the rank $g$ of the one-dimensional homo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06759","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":""},"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"}