{"paper":{"title":"A near optimal algorithm for finding Euclidean shortest path in polygonal domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Rajasekhar Inkulu, Sanjiv Kapoor, S. N. Maheshwari","submitted_at":"2010-11-30T08:42:45Z","abstract_excerpt":"We present an algorithm to find an {\\it Euclidean Shortest Path} from a source vertex $s$ to a sink vertex $t$ in the presence of obstacles in $\\Re^2$. Our algorithm takes $O(T+m(\\lg{m})(\\lg{n}))$ time and $O(n)$ space. Here, $O(T)$ is the time to triangulate the polygonal region, $m$ is the number of obstacles, and $n$ is the number of vertices. This bound is close to the known lower bound of $O(n+m\\lg{m})$ time and $O(n)$ space. Our approach involve progressing shortest path wavefront as in continuous Dijkstra-type method, and confining its expansion to regions of interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6481","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"}