A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon
Let P be a closed simple polygon with n vertices. For any two points in P , the geodesic distance between them is the length of the shortest path that connects them among all paths contained in P . The geodesic center of P is the unique point in P that minimizes the largest geodesic distance to all...
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| Veröffentlicht in: | Discrete & computational geometry 2016-12, Vol.56 (4), p.836-859 |
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| creator | Ahn, Hee-Kap Barba, Luis Bose, Prosenjit De Carufel, Jean-Lou Korman, Matias Oh, Eunjin |
| description | Let
P
be a closed simple polygon with
n
vertices. For any two points in
P
, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in
P
. The geodesic center of
P
is the unique point in
P
that minimizes the largest geodesic distance to all other points of
P
. In 1989, Pollack et al. (Discrete Comput Geom 4(1): 611–626,
1989
) showed an
O
(
n
log
n
)
-time algorithm that computes the geodesic center of
P
. Since then, a longstanding question has been whether this running time can be improved. In this paper we affirmatively answer this question and present a deterministic linear-time algorithm to solve this problem. |
| doi_str_mv | 10.1007/s00454-016-9796-0 |
| format | Article |
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P
be a closed simple polygon with
n
vertices. For any two points in
P
, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in
P
. The geodesic center of
P
is the unique point in
P
that minimizes the largest geodesic distance to all other points of
P
. In 1989, Pollack et al. (Discrete Comput Geom 4(1): 611–626,
1989
) showed an
O
(
n
log
n
)
-time algorithm that computes the geodesic center of
P
. Since then, a longstanding question has been whether this running time can be improved. In this paper we affirmatively answer this question and present a deterministic linear-time algorithm to solve this problem.</description><identifier>ISSN: 0179-5376</identifier><identifier>EISSN: 1432-0444</identifier><identifier>DOI: 10.1007/s00454-016-9796-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Combinatorics ; Computational Mathematics and Numerical Analysis ; Mathematics ; Mathematics and Statistics ; Run time (computers) ; Running ; Shortest-path problems ; Traveling salesman problem</subject><ispartof>Discrete & computational geometry, 2016-12, Vol.56 (4), p.836-859</ispartof><rights>Springer Science+Business Media New York 2016</rights><rights>Discrete & Computational Geometry is a copyright of Springer, 2016.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-48b3a027f91133be89ad6899d69525d28d0504f5c9667669de812d665f770f4d3</citedby><cites>FETCH-LOGICAL-c382t-48b3a027f91133be89ad6899d69525d28d0504f5c9667669de812d665f770f4d3</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/s00454-016-9796-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00454-016-9796-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Ahn, Hee-Kap</creatorcontrib><creatorcontrib>Barba, Luis</creatorcontrib><creatorcontrib>Bose, Prosenjit</creatorcontrib><creatorcontrib>De Carufel, Jean-Lou</creatorcontrib><creatorcontrib>Korman, Matias</creatorcontrib><creatorcontrib>Oh, Eunjin</creatorcontrib><title>A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon</title><title>Discrete & computational geometry</title><addtitle>Discrete Comput Geom</addtitle><description>Let
P
be a closed simple polygon with
n
vertices. For any two points in
P
, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in
P
. The geodesic center of
P
is the unique point in
P
that minimizes the largest geodesic distance to all other points of
P
. In 1989, Pollack et al. (Discrete Comput Geom 4(1): 611–626,
1989
) showed an
O
(
n
log
n
)
-time algorithm that computes the geodesic center of
P
. Since then, a longstanding question has been whether this running time can be improved. In this paper we affirmatively answer this question and present a deterministic linear-time algorithm to solve this problem.</description><subject>Algorithms</subject><subject>Combinatorics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Run time (computers)</subject><subject>Running</subject><subject>Shortest-path problems</subject><subject>Traveling salesman problem</subject><issn>0179-5376</issn><issn>1432-0444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kD1PwzAURS0EEqXwA9gsMRuev-OxiqAgVQKJMltpbLepkrjY6dB_T6owsDC95dx79Q5C9xQeKYB-ygBCCgJUEaONInCBZlRwRkAIcYlmQLUhkmt1jW5y3sOIGyhmqFzgVdP7KpF103m8aLcxNcOuwyEmPOw8XvrofG5qXPp-8AnHgCv82XSH1uOP2J62sb9FV6Fqs7_7vXP09fK8Ll_J6n35Vi5WpOYFG4goNrwCpoOhlPONL0zlVGGMU0Yy6VjhQIIIsjZKaaWM8wVlTikZtIYgHJ-jh6n3kOL30efB7uMx9eOkpeMzXIIUYqToRNUp5px8sIfUdFU6WQr27MpOruzoyp5dWRgzbMrkke23Pv1p_jf0AwWaaT4</recordid><startdate>20161201</startdate><enddate>20161201</enddate><creator>Ahn, Hee-Kap</creator><creator>Barba, Luis</creator><creator>Bose, Prosenjit</creator><creator>De Carufel, Jean-Lou</creator><creator>Korman, Matias</creator><creator>Oh, Eunjin</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20161201</creationdate><title>A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon</title><author>Ahn, Hee-Kap ; Barba, Luis ; Bose, Prosenjit ; De Carufel, Jean-Lou ; Korman, Matias ; Oh, Eunjin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-48b3a027f91133be89ad6899d69525d28d0504f5c9667669de812d665f770f4d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Algorithms</topic><topic>Combinatorics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Run time (computers)</topic><topic>Running</topic><topic>Shortest-path problems</topic><topic>Traveling salesman problem</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ahn, Hee-Kap</creatorcontrib><creatorcontrib>Barba, Luis</creatorcontrib><creatorcontrib>Bose, Prosenjit</creatorcontrib><creatorcontrib>De Carufel, Jean-Lou</creatorcontrib><creatorcontrib>Korman, Matias</creatorcontrib><creatorcontrib>Oh, Eunjin</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>ProQuest Research Library</collection><collection>ProQuest Science Journals</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Research Library China</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Discrete & computational geometry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ahn, Hee-Kap</au><au>Barba, Luis</au><au>Bose, Prosenjit</au><au>De Carufel, Jean-Lou</au><au>Korman, Matias</au><au>Oh, Eunjin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon</atitle><jtitle>Discrete & computational geometry</jtitle><stitle>Discrete Comput Geom</stitle><date>2016-12-01</date><risdate>2016</risdate><volume>56</volume><issue>4</issue><spage>836</spage><epage>859</epage><pages>836-859</pages><issn>0179-5376</issn><eissn>1432-0444</eissn><abstract>Let
P
be a closed simple polygon with
n
vertices. For any two points in
P
, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in
P
. The geodesic center of
P
is the unique point in
P
that minimizes the largest geodesic distance to all other points of
P
. In 1989, Pollack et al. (Discrete Comput Geom 4(1): 611–626,
1989
) showed an
O
(
n
log
n
)
-time algorithm that computes the geodesic center of
P
. Since then, a longstanding question has been whether this running time can be improved. In this paper we affirmatively answer this question and present a deterministic linear-time algorithm to solve this problem.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00454-016-9796-0</doi><tpages>24</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
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| ispartof | Discrete & computational geometry, 2016-12, Vol.56 (4), p.836-859 |
| issn | 0179-5376 1432-0444 |
| language | eng |
| recordid | cdi_proquest_journals_1908350544 |
| source | SpringerNature Journals |
| subjects | Algorithms Combinatorics Computational Mathematics and Numerical Analysis Mathematics Mathematics and Statistics Run time (computers) Running Shortest-path problems Traveling salesman problem |
| title | A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon |
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