{"id":13230,"date":"2021-12-07T21:04:48","date_gmt":"2021-12-08T02:04:48","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=13230"},"modified":"2021-12-07T21:04:48","modified_gmt":"2021-12-08T02:04:48","slug":"tr-07-22-spanners-of-complete-k-partite-geometric-graphs","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2007\/tr-07-22-spanners-of-complete-k-partite-geometric-graphs\/","title":{"rendered":"TR-07-22: Spanners of complete k-Partite Geometric Graphs"},"content":{"rendered":"

Carleton University
\nTechnical Report<\/a> TR-07-22
\nDecember 5, 2007<\/p>\n

Spanners of complete k-Partite Geometric Graphs<\/h2>\n
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Prosenjit Bose, Paz Carmi, Mathieu Couture, Anil Maheshwari, Pat Morin, Michiel Smid<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

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Abstract<\/h3>\n

We address the following problem: Given a complete $k$-partite geometric graph $K$ whose vertex set is a set of $n$ points in $\\mathbb{R}^d$, compute a spanner of $K$ that has a “small” stretch factor and “few” edges. We present two algorithms for this problem. The first algorithm computes a $(5+\\epsilon)$-spanner of $K$ with $O(n)$ edges in $O(n \\log n)$ time. The second algorithm computes a $(3+\\epsilon)$-spanner of $K$ with $O(n \\log n)$ edges in $O(n \\log n)$ time. The latter result is optimal: We show that for any $2 \\leq k \\leq n – \\Theta(\\sqrt{n \\log n} )$, spanners with $O(n \\log n)$ edges and stretch factor less than $3$ do not exist for all complete $k$-partite geometric graphs.<\/p>\n

TR-07-22.pdf<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Carleton University Technical Report TR-07-22 December 5, 2007 Spanners of complete k-Partite Geometric Graphs Prosenjit Bose, Paz Carmi, Mathieu Couture, Anil Maheshwari, Pat Morin, Michiel Smid Abstract We address the following problem: Given a complete $k$-partite geometric graph $K$ whose vertex set is a set of $n$ points in $\\mathbb{R}^d$, compute a spanner of $K$ […]<\/p>\n","protected":false},"author":49,"featured_media":0,"parent":12385,"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-07-22: Spanners of complete k-Partite Geometric Graphs - 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