{"paper":{"title":"A Simple Algorithm For Replacement Paths Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anjeneya Swami Kare","submitted_at":"2015-11-21T17:32:42Z","abstract_excerpt":"Let G=(V,E)(|V|=n and |E|=m) be an undirected graph with positive edge weights. Let P_{G}(s, t) be a shortest s-t path in G. Let l be the number of edges in P_{G}(s, t). The \\emph{Edge Replacement Path} problem is to compute a shortest s-t path in G\\{e}, for every edge e in P_{G}(s, t). The \\emph{Node Replacement Path} problem is to compute a shortest s-t path in G\\{v}, for every vertex v in P_{G}(s, t). In this paper we present an O(T_{SPT}(G)+m+l^2) time and O(m+l^2) space algorithm for both the problems. Where, T_{SPT}(G) is the asymptotic time to compute a single source shortest path tree "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06905","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"}