Random half-integral polytopes
We show that polytopes obtained as the convex hull of a random set of half-integral points of the 0/1 cube have rank as high as Ω ( log n / log log n ) with positive probability—even if the size of the set relative to the total number of half-integral points of the cube tends to 0. The high rank is...
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| Veröffentlicht in: | Operations research letters 2011-05, Vol.39 (3), p.204-207 |
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| container_end_page | 207 |
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| container_title | Operations research letters |
| container_volume | 39 |
| creator | Braun, Gábor Pokutta, Sebastian |
| description | We show that polytopes obtained as the convex hull of a random set of half-integral points of the 0/1 cube have rank as high as
Ω
(
log
n
/
log
log
n
)
with positive probability—even if the size of the set relative to the total number of half-integral points of the cube tends to 0. The high rank is due to certain obstructions. We determine the exact threshold number, when those cease to exist. |
| doi_str_mv | 10.1016/j.orl.2011.03.003 |
| format | Article |
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Ω
(
log
n
/
log
log
n
)
with positive probability—even if the size of the set relative to the total number of half-integral points of the cube tends to 0. The high rank is due to certain obstructions. We determine the exact threshold number, when those cease to exist.</description><identifier>ISSN: 0167-6377</identifier><identifier>EISSN: 1872-7468</identifier><identifier>DOI: 10.1016/j.orl.2011.03.003</identifier><identifier>CODEN: ORLED5</identifier><language>eng</language><publisher>Oxford: Elsevier B.V</publisher><subject>Applied sciences ; Cubes ; Cutting-plane procedures ; Exact sciences and technology ; Hulls ; Hulls (structures) ; Mathematical programming ; Obstructions ; Operational research and scientific management ; Operational research. Management science ; Operations research ; Polytopes ; Random half-integral polytopes ; Rank lower bounds ; Thresholds</subject><ispartof>Operations research letters, 2011-05, Vol.39 (3), p.204-207</ispartof><rights>2011 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c391t-28287f048eeb0732ce150617f0912f0e505e40bd360b792ac3fbecff7bbd7f463</citedby><cites>FETCH-LOGICAL-c391t-28287f048eeb0732ce150617f0912f0e505e40bd360b792ac3fbecff7bbd7f463</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.orl.2011.03.003$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24235200$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Braun, Gábor</creatorcontrib><creatorcontrib>Pokutta, Sebastian</creatorcontrib><title>Random half-integral polytopes</title><title>Operations research letters</title><description>We show that polytopes obtained as the convex hull of a random set of half-integral points of the 0/1 cube have rank as high as
Ω
(
log
n
/
log
log
n
)
with positive probability—even if the size of the set relative to the total number of half-integral points of the cube tends to 0. The high rank is due to certain obstructions. We determine the exact threshold number, when those cease to exist.</description><subject>Applied sciences</subject><subject>Cubes</subject><subject>Cutting-plane procedures</subject><subject>Exact sciences and technology</subject><subject>Hulls</subject><subject>Hulls (structures)</subject><subject>Mathematical programming</subject><subject>Obstructions</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Operations research</subject><subject>Polytopes</subject><subject>Random half-integral polytopes</subject><subject>Rank lower bounds</subject><subject>Thresholds</subject><issn>0167-6377</issn><issn>1872-7468</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LxDAUxIMouFY_gBfZi-Cl9SVpkxZPsvgPFgTRc0jTF83SbWrSFfbbm2UXj54eDL-ZxwwhlxQKClTcrgof-oIBpQXwAoAfkRmtJctlKepjMkuMzAWX8pScxbgCAFnTekau3vTQ-fX8S_c2d8OEn0H389H328mPGM_JidV9xIvDzcjH48P74jlfvj69LO6XueENnXJWs1paKGvEFiRnBmkFgiapocwCVlBhCW3HBbSyYdpw26KxVrZtJ20peEZu9rlj8N8bjJNau2iw7_WAfhNV6tiIphJMJpTuURN8jAGtGoNb67BN0I4TaqXSFmq3hQKu0hbJc32I19GkpkEPxsU_IysZr1gCM3K35zB1_XEYVDQOB4OdC2gm1Xn3z5dfVxlyXw</recordid><startdate>20110501</startdate><enddate>20110501</enddate><creator>Braun, Gábor</creator><creator>Pokutta, Sebastian</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TA</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JG9</scope><scope>KR7</scope></search><sort><creationdate>20110501</creationdate><title>Random half-integral polytopes</title><author>Braun, Gábor ; Pokutta, Sebastian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c391t-28287f048eeb0732ce150617f0912f0e505e40bd360b792ac3fbecff7bbd7f463</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Applied sciences</topic><topic>Cubes</topic><topic>Cutting-plane procedures</topic><topic>Exact sciences and technology</topic><topic>Hulls</topic><topic>Hulls (structures)</topic><topic>Mathematical programming</topic><topic>Obstructions</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Operations research</topic><topic>Polytopes</topic><topic>Random half-integral polytopes</topic><topic>Rank lower bounds</topic><topic>Thresholds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Braun, Gábor</creatorcontrib><creatorcontrib>Pokutta, Sebastian</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Materials Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Operations research letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Braun, Gábor</au><au>Pokutta, Sebastian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Random half-integral polytopes</atitle><jtitle>Operations research letters</jtitle><date>2011-05-01</date><risdate>2011</risdate><volume>39</volume><issue>3</issue><spage>204</spage><epage>207</epage><pages>204-207</pages><issn>0167-6377</issn><eissn>1872-7468</eissn><coden>ORLED5</coden><abstract>We show that polytopes obtained as the convex hull of a random set of half-integral points of the 0/1 cube have rank as high as
Ω
(
log
n
/
log
log
n
)
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| fulltext | fulltext |
| identifier | ISSN: 0167-6377 |
| ispartof | Operations research letters, 2011-05, Vol.39 (3), p.204-207 |
| issn | 0167-6377 1872-7468 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1019695627 |
| source | Elsevier ScienceDirect Journals |
| subjects | Applied sciences Cubes Cutting-plane procedures Exact sciences and technology Hulls Hulls (structures) Mathematical programming Obstructions Operational research and scientific management Operational research. Management science Operations research Polytopes Random half-integral polytopes Rank lower bounds Thresholds |
| title | Random half-integral polytopes |
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