Maximum weight triangulation and graph drawing
In this paper, we investigate the maximum weight triangulation of a convex polygon and its application to graph drawing. We can find the maximum weight triangulation of a special n-gon which inscribed on a circle in O(n 2) time. The complexity of this algorithm can be reduced to O(n) if the polygon...
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| Veröffentlicht in: | Information processing letters 1999-04, Vol.70 (1), p.17-22 |
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| creator | Wang, Cao An Chin, Francis Y. Yang, Bo Ting |
| description | In this paper, we investigate the maximum weight triangulation of a convex polygon and its application to graph drawing. We can find the maximum weight triangulation of a special
n-gon which inscribed on a circle in
O(n
2)
time. The complexity of this algorithm can be reduced to
O(n)
if the polygon is regular. The algorithm also produces a triangulation approximating the maximum weight triangulation of a convex
n-gon with weight ratio 0.5. We further show that a tree always admits a maximum weight drawing if the internal nodes of the tree connect to at most 2 non-leaf nodes, and the drawing can be done in
O(n)
time. Finally, we prove a property of maximum planar graphs which do not admit a maximum weight drawing on any convex point set. |
| doi_str_mv | 10.1016/S0020-0190(99)00037-X |
| format | Article |
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n-gon which inscribed on a circle in
O(n
2)
time. The complexity of this algorithm can be reduced to
O(n)
if the polygon is regular. The algorithm also produces a triangulation approximating the maximum weight triangulation of a convex
n-gon with weight ratio 0.5. We further show that a tree always admits a maximum weight drawing if the internal nodes of the tree connect to at most 2 non-leaf nodes, and the drawing can be done in
O(n)
time. Finally, we prove a property of maximum planar graphs which do not admit a maximum weight drawing on any convex point set.</description><identifier>ISSN: 0020-0190</identifier><identifier>EISSN: 1872-6119</identifier><identifier>DOI: 10.1016/S0020-0190(99)00037-X</identifier><identifier>CODEN: IFPLAT</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Algorithmics. Computability. Computer arithmetics ; Algorithms ; Applied sciences ; Approximation ; Computer science; control theory; systems ; Exact sciences and technology ; Geometry ; Graph drawing ; Graphs ; Information retrieval. Graph ; Maximum weight triangulation ; Studies ; Theoretical computing ; Weights & measures</subject><ispartof>Information processing letters, 1999-04, Vol.70 (1), p.17-22</ispartof><rights>1999 Elsevier Science B.V.</rights><rights>1999 INIST-CNRS</rights><rights>Copyright Elsevier Sequoia S.A. Apr 16, 1999</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-1c77c80c0fad63466024c888516ea53a7df8d7f3a607abcd777b311b412f635f3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/S0020-0190(99)00037-X$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=1806999$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Wang, Cao An</creatorcontrib><creatorcontrib>Chin, Francis Y.</creatorcontrib><creatorcontrib>Yang, Bo Ting</creatorcontrib><title>Maximum weight triangulation and graph drawing</title><title>Information processing letters</title><description>In this paper, we investigate the maximum weight triangulation of a convex polygon and its application to graph drawing. We can find the maximum weight triangulation of a special
n-gon which inscribed on a circle in
O(n
2)
time. The complexity of this algorithm can be reduced to
O(n)
if the polygon is regular. The algorithm also produces a triangulation approximating the maximum weight triangulation of a convex
n-gon with weight ratio 0.5. We further show that a tree always admits a maximum weight drawing if the internal nodes of the tree connect to at most 2 non-leaf nodes, and the drawing can be done in
O(n)
time. Finally, we prove a property of maximum planar graphs which do not admit a maximum weight drawing on any convex point set.</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Approximation</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Geometry</subject><subject>Graph drawing</subject><subject>Graphs</subject><subject>Information retrieval. Graph</subject><subject>Maximum weight triangulation</subject><subject>Studies</subject><subject>Theoretical computing</subject><subject>Weights & measures</subject><issn>0020-0190</issn><issn>1872-6119</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><recordid>eNqFkE1LAzEYhIMoWKs_QVjEgx62vtnsJpuTSPELKh5U6C28zUeb0u7WZNfqv3fbih49zeWZGWYIOaUwoED51QtABilQCRdSXgIAE-l4j_RoKbKUUyr3Se8XOSRHMc47iOdM9MjgCT_9sl0ma-unsyZpgsdq2i6w8XWVYGWSacDVLDEB176aHpMDh4toT360T97ubl-HD-no-f5xeDNKNeOsSakWQpegwaHhLOccslyXZVlQbrFgKIwrjXAMOQicaCOEmDBKJznNHGeFY31ytstdhfq9tbFR87oNVVepMiYyISXNO6jYQTrUMQbr1Cr4JYYvRUFtnlHbZ9RmtpJSbZ9R4853_hOOUePCBay0j3_mEriUssOud5jthn54G1TU3lbaGh-sbpSp_T9F39Hbdjg</recordid><startdate>19990416</startdate><enddate>19990416</enddate><creator>Wang, Cao An</creator><creator>Chin, Francis Y.</creator><creator>Yang, Bo Ting</creator><general>Elsevier B.V</general><general>Elsevier Science</general><general>Elsevier Sequoia S.A</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19990416</creationdate><title>Maximum weight triangulation and graph drawing</title><author>Wang, Cao An ; Chin, Francis Y. ; Yang, Bo Ting</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-1c77c80c0fad63466024c888516ea53a7df8d7f3a607abcd777b311b412f635f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><topic>Algorithmics. Computability. Computer arithmetics</topic><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Approximation</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Geometry</topic><topic>Graph drawing</topic><topic>Graphs</topic><topic>Information retrieval. Graph</topic><topic>Maximum weight triangulation</topic><topic>Studies</topic><topic>Theoretical computing</topic><topic>Weights & measures</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Cao An</creatorcontrib><creatorcontrib>Chin, Francis Y.</creatorcontrib><creatorcontrib>Yang, Bo Ting</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science 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><jtitle>Information processing letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Cao An</au><au>Chin, Francis Y.</au><au>Yang, Bo Ting</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Maximum weight triangulation and graph drawing</atitle><jtitle>Information processing letters</jtitle><date>1999-04-16</date><risdate>1999</risdate><volume>70</volume><issue>1</issue><spage>17</spage><epage>22</epage><pages>17-22</pages><issn>0020-0190</issn><eissn>1872-6119</eissn><coden>IFPLAT</coden><abstract>In this paper, we investigate the maximum weight triangulation of a convex polygon and its application to graph drawing. We can find the maximum weight triangulation of a special
n-gon which inscribed on a circle in
O(n
2)
time. The complexity of this algorithm can be reduced to
O(n)
if the polygon is regular. The algorithm also produces a triangulation approximating the maximum weight triangulation of a convex
n-gon with weight ratio 0.5. We further show that a tree always admits a maximum weight drawing if the internal nodes of the tree connect to at most 2 non-leaf nodes, and the drawing can be done in
O(n)
time. Finally, we prove a property of maximum planar graphs which do not admit a maximum weight drawing on any convex point set.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/S0020-0190(99)00037-X</doi><tpages>6</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0020-0190 |
| ispartof | Information processing letters, 1999-04, Vol.70 (1), p.17-22 |
| issn | 0020-0190 1872-6119 |
| language | eng |
| recordid | cdi_proquest_journals_237279914 |
| source | Access via ScienceDirect (Elsevier) |
| subjects | Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Approximation Computer science control theory systems Exact sciences and technology Geometry Graph drawing Graphs Information retrieval. Graph Maximum weight triangulation Studies Theoretical computing Weights & measures |
| title | Maximum weight triangulation and graph drawing |
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