A quick estimate for the volume of a polyhedron
Let P be a bounded polyhedron defined as the intersection of the non-negative orthant ℝ + n and an affine subspace of codimension m in ℝ n . We show that a simple and computationally efficient formula approximates the volume of P within a factor of γ m , where γ > 0 is an absolute constant. The f...
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| Veröffentlicht in: | Israel journal of mathematics 2024, Vol.262 (1), p.449-473 |
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| container_title | Israel journal of mathematics |
| container_volume | 262 |
| creator | Barvinok, Alexander Rudelson, Mark |
| description | Let
P
be a bounded polyhedron defined as the intersection of the non-negative orthant ℝ
+
n
and an affine subspace of codimension
m
in ℝ
n
. We show that a simple and computationally efficient formula approximates the volume of
P
within a factor of
γ
m
, where
γ
> 0 is an absolute constant. The formula provides the best known estimate for the volume of transportation polytopes from a wide family. |
| doi_str_mv | 10.1007/s11856-024-2615-z |
| format | Article |
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P
be a bounded polyhedron defined as the intersection of the non-negative orthant ℝ
+
n
and an affine subspace of codimension
m
in ℝ
n
. We show that a simple and computationally efficient formula approximates the volume of
P
within a factor of
γ
m
, where
γ
> 0 is an absolute constant. The formula provides the best known estimate for the volume of transportation polytopes from a wide family.</description><identifier>ISSN: 0021-2172</identifier><identifier>EISSN: 1565-8511</identifier><identifier>DOI: 10.1007/s11856-024-2615-z</identifier><language>eng</language><publisher>Jerusalem: The Hebrew University Magnes Press</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Group Theory and Generalizations ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Polyhedra ; Polytopes ; Theoretical</subject><ispartof>Israel journal of mathematics, 2024, Vol.262 (1), p.449-473</ispartof><rights>The Hebrew University of Jerusalem 2024</rights><rights>The Hebrew University of Jerusalem 2024.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-caf84b5f25ee7fc038b12f306b148fcaf1d957e35ee1c117a10bb1bc885de793</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11856-024-2615-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11856-024-2615-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Barvinok, Alexander</creatorcontrib><creatorcontrib>Rudelson, Mark</creatorcontrib><title>A quick estimate for the volume of a polyhedron</title><title>Israel journal of mathematics</title><addtitle>Isr. J. Math</addtitle><description>Let
P
be a bounded polyhedron defined as the intersection of the non-negative orthant ℝ
+
n
and an affine subspace of codimension
m
in ℝ
n
. We show that a simple and computationally efficient formula approximates the volume of
P
within a factor of
γ
m
, where
γ
> 0 is an absolute constant. The formula provides the best known estimate for the volume of transportation polytopes from a wide family.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Group Theory and Generalizations</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Polyhedra</subject><subject>Polytopes</subject><subject>Theoretical</subject><issn>0021-2172</issn><issn>1565-8511</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1kEFPAjEQhRujiYj-AG9NPFdm2u22HAlRMSHxwr3Z7bYCLhTaXRP49ZasiSfnMod5783MR8gjwjMCqElC1LJkwAvGS5TsfEVGKEvJtES8JiMAjoyj4rfkLqUtgBQKxYhMZvTYb-wXdanb7KrOUR8i7daOfoe23zkaPK3oIbSntWti2N-TG1-1yT389jFZvb6s5gu2_Hh7n8-WzPJSd8xWXhe19Fw6p7wFoWvkXkBZY6F9nmIzlcqJPEaLqCqEusbaai0bp6ZiTJ6G2EMMxz7fZrahj_u80QhEDtNcKqtwUNkYUorOm0PMT8STQTAXLGbAYjIWc8FiztnDB0_K2v2ni3_J_5t-AGfkZOA</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Barvinok, Alexander</creator><creator>Rudelson, Mark</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2024</creationdate><title>A quick estimate for the volume of a polyhedron</title><author>Barvinok, Alexander ; Rudelson, Mark</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-caf84b5f25ee7fc038b12f306b148fcaf1d957e35ee1c117a10bb1bc885de793</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Group Theory and Generalizations</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Polyhedra</topic><topic>Polytopes</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Barvinok, Alexander</creatorcontrib><creatorcontrib>Rudelson, Mark</creatorcontrib><collection>CrossRef</collection><jtitle>Israel journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Barvinok, Alexander</au><au>Rudelson, Mark</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A quick estimate for the volume of a polyhedron</atitle><jtitle>Israel journal of mathematics</jtitle><stitle>Isr. J. Math</stitle><date>2024</date><risdate>2024</risdate><volume>262</volume><issue>1</issue><spage>449</spage><epage>473</epage><pages>449-473</pages><issn>0021-2172</issn><eissn>1565-8511</eissn><abstract>Let
P
be a bounded polyhedron defined as the intersection of the non-negative orthant ℝ
+
n
and an affine subspace of codimension
m
in ℝ
n
. We show that a simple and computationally efficient formula approximates the volume of
P
within a factor of
γ
m
, where
γ
> 0 is an absolute constant. The formula provides the best known estimate for the volume of transportation polytopes from a wide family.</abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11856-024-2615-z</doi><tpages>25</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-2172 |
| ispartof | Israel journal of mathematics, 2024, Vol.262 (1), p.449-473 |
| issn | 0021-2172 1565-8511 |
| language | eng |
| recordid | cdi_proquest_journals_3112099997 |
| source | SpringerLink Journals |
| subjects | Algebra Analysis Applications of Mathematics Group Theory and Generalizations Mathematical and Computational Physics Mathematics Mathematics and Statistics Polyhedra Polytopes Theoretical |
| title | A quick estimate for the volume of a polyhedron |
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