{"id":13352,"date":"2021-12-09T20:54:25","date_gmt":"2021-12-10T01:54:25","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=13352"},"modified":"2021-12-09T20:54:25","modified_gmt":"2021-12-10T01:54:25","slug":"tr-11-02-an-approximation-algorithm-for-computing-shortest-paths-in-weighted-3-d-domains","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2011\/tr-11-02-an-approximation-algorithm-for-computing-shortest-paths-in-weighted-3-d-domains\/","title":{"rendered":"TR-11-02: An Approximation Algorithm for Computing Shortest Paths in Weighted 3-d Domains"},"content":{"rendered":"

Carleton University
\nTechnical Report<\/a> TR-11-02
\nFebruary 27, 2011<\/p>\n

An Approximation Algorithm for Computing Shortest Paths in Weighted 3-d Domains<\/h2>\n
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Lyudmil Aleksandrov, Hristo Djidjev, Anil Maheshwari, Jorg-Rudiger Sack<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Abstract<\/h3>\n

We present the first polynomial time approximation algorithm for computing shortest paths in weighted three-dimensional domains. Given a polyhedral domain D, consisting of n tetrahedra with positive weights, and a real number $epsin(0,1)$, our algorithm constructs paths in D from a fixed source vertex to all vertices of D, whose costs are at most $1+eps$ times the costs of (weighted) shortest paths, in $O(C(D)frac{n}{eps^{2.5}}logfrac{n}{eps}log^3frac{1}{eps})$ time, where $C(D)$ is a geometric parameter related to the aspect ratios of tetrahedra. The efficiency of the proposed algorithm is based on an in-depth study of the local behavior of geodesic paths and additive Voronoi diagrams in weighted three-dimensional domains, which are of independent interest. The paper extends the results of Aleksandrov, Maheshwari and Sack [JACM 2005] to three dimensions.<\/p>\n

TR-11-02.pdf<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Carleton University Technical Report TR-11-02 February 27, 2011 An Approximation Algorithm for Computing Shortest Paths in Weighted 3-d Domains Lyudmil Aleksandrov, Hristo Djidjev, Anil Maheshwari, Jorg-Rudiger Sack Abstract We present the first polynomial time approximation algorithm for computing shortest paths in weighted three-dimensional domains. Given a polyhedral domain D, consisting of n tetrahedra with positive […]<\/p>\n","protected":false},"author":49,"featured_media":0,"parent":12489,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":"","_links_to":"","_links_to_target":""},"yoast_head":"\nTR-11-02: An Approximation Algorithm for Computing Shortest Paths in Weighted 3-d Domains - School of Computer Science<\/title>\n<meta name=\"description\" content=\"Carleton University Technical Report TR-11-02 February 27, 2011 An Approximation Algorithm for Computing Shortest Paths in Weighted 3-d Domains Lyudmil\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2011\/tr-11-02-an-approximation-algorithm-for-computing-shortest-paths-in-weighted-3-d-domains\/\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2011\/tr-11-02-an-approximation-algorithm-for-computing-shortest-paths-in-weighted-3-d-domains\/\",\"url\":\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2011\/tr-11-02-an-approximation-algorithm-for-computing-shortest-paths-in-weighted-3-d-domains\/\",\"name\":\"TR-11-02: An Approximation Algorithm for Computing Shortest Paths in Weighted 3-d Domains - 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