The smallest pair of noncrossing paths in a rectilinear polygon
Smallest rectilinear paths are rectilinear paths with simultaneous minimum numbers of bends and minimum lengths. Given two pairs of terminals within a rectilinear polygon, the authors derive an algorithm to find a pair of noncrossing rectilinear paths within the polygon such that the total number of...
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| Veröffentlicht in: | IEEE transactions on computers 1997-08, Vol.46 (8), p.930-941 |
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| container_title | IEEE transactions on computers |
| container_volume | 46 |
| creator | Yang, C.D. |
| description | Smallest rectilinear paths are rectilinear paths with simultaneous minimum numbers of bends and minimum lengths. Given two pairs of terminals within a rectilinear polygon, the authors derive an algorithm to find a pair of noncrossing rectilinear paths within the polygon such that the total number of bends and the total length are both minimized. Although a smallest rectilinear path between two terminals in a rectilinear polygon always exists, they show that such a smallest pair may not exist for some problem instances. In that case, the algorithm presented will find, among all noncrossing paths with a minimum total number of bends, a pair whose total length is the shortest, or find, among all noncrossing paths with a minimum total length, a pair whose total number of bends is minimized. They provide a simple linear time and space algorithm based on the fact that there are only a limited number of configurations of such a solution pair. |
| doi_str_mv | 10.1109/12.609280 |
| format | Article |
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Given two pairs of terminals within a rectilinear polygon, the authors derive an algorithm to find a pair of noncrossing rectilinear paths within the polygon such that the total number of bends and the total length are both minimized. Although a smallest rectilinear path between two terminals in a rectilinear polygon always exists, they show that such a smallest pair may not exist for some problem instances. In that case, the algorithm presented will find, among all noncrossing paths with a minimum total number of bends, a pair whose total length is the shortest, or find, among all noncrossing paths with a minimum total length, a pair whose total number of bends is minimized. They provide a simple linear time and space algorithm based on the fact that there are only a limited number of configurations of such a solution pair.</description><identifier>ISSN: 0018-9340</identifier><identifier>EISSN: 1557-9956</identifier><identifier>DOI: 10.1109/12.609280</identifier><identifier>CODEN: ITCOB4</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Computational geometry ; Cost function ; Design. Technologies. Operation analysis. Testing ; Electronics ; Exact sciences and technology ; Integrated circuits ; Joining processes ; Motion planning ; Packaging ; Path planning ; Production facilities ; Robot motion ; Routing ; Semiconductor electronics. Microelectronics. Optoelectronics. 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Given two pairs of terminals within a rectilinear polygon, the authors derive an algorithm to find a pair of noncrossing rectilinear paths within the polygon such that the total number of bends and the total length are both minimized. Although a smallest rectilinear path between two terminals in a rectilinear polygon always exists, they show that such a smallest pair may not exist for some problem instances. In that case, the algorithm presented will find, among all noncrossing paths with a minimum total number of bends, a pair whose total length is the shortest, or find, among all noncrossing paths with a minimum total length, a pair whose total number of bends is minimized. They provide a simple linear time and space algorithm based on the fact that there are only a limited number of configurations of such a solution pair.</description><subject>Applied sciences</subject><subject>Computational geometry</subject><subject>Cost function</subject><subject>Design. Technologies. Operation analysis. Testing</subject><subject>Electronics</subject><subject>Exact sciences and technology</subject><subject>Integrated circuits</subject><subject>Joining processes</subject><subject>Motion planning</subject><subject>Packaging</subject><subject>Path planning</subject><subject>Production facilities</subject><subject>Robot motion</subject><subject>Routing</subject><subject>Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices</subject><subject>Very large scale integration</subject><issn>0018-9340</issn><issn>1557-9956</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1997</creationdate><recordtype>article</recordtype><recordid>eNo9kL1PwzAQxS0EEqUwsDJ5QEgMKefYcewJoYovqRJLmSNjO62R4wQ7HfrfY0jV6aR3v3t69xC6JrAgBOQDKRccZCngBM1IVdWFlBU_RTMAIgpJGZyji5S-AYCXIGfocb21OHXKe5tGPCgXcd_i0Acd-5Rc2GRt3CbsAlY4Wj0674JVEQ-932_6cInOWuWTvTrMOfp8eV4v34rVx-v78mlVaAp8LIgBw3Qtai5yECIY02AMrRnVQoIkXy0YzYwVLUAFtCbUVEYRmlXJgBM6R3eT7xD7n13O2nQuaeu9CrbfpaYUnHPKeAbvJ_D_gWjbZoiuU3HfEGj-KmpI2UwVZfb2YKqSVr6NKmiXjgdlLTJYZ-xmwpy19rg9ePwCgFpsEw</recordid><startdate>19970801</startdate><enddate>19970801</enddate><creator>Yang, C.D.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</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>19970801</creationdate><title>The smallest pair of noncrossing paths in a rectilinear polygon</title><author>Yang, C.D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c306t-1d0d4c787680181844c0dd3743c89091bf0dc4de8f00503713d5da130dc940613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1997</creationdate><topic>Applied sciences</topic><topic>Computational geometry</topic><topic>Cost function</topic><topic>Design. Technologies. Operation analysis. Testing</topic><topic>Electronics</topic><topic>Exact sciences and technology</topic><topic>Integrated circuits</topic><topic>Joining processes</topic><topic>Motion planning</topic><topic>Packaging</topic><topic>Path planning</topic><topic>Production facilities</topic><topic>Robot motion</topic><topic>Routing</topic><topic>Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices</topic><topic>Very large scale integration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yang, C.D.</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>IEEE transactions on computers</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Yang, C.D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The smallest pair of noncrossing paths in a rectilinear polygon</atitle><jtitle>IEEE transactions on computers</jtitle><stitle>TC</stitle><date>1997-08-01</date><risdate>1997</risdate><volume>46</volume><issue>8</issue><spage>930</spage><epage>941</epage><pages>930-941</pages><issn>0018-9340</issn><eissn>1557-9956</eissn><coden>ITCOB4</coden><abstract>Smallest rectilinear paths are rectilinear paths with simultaneous minimum numbers of bends and minimum lengths. Given two pairs of terminals within a rectilinear polygon, the authors derive an algorithm to find a pair of noncrossing rectilinear paths within the polygon such that the total number of bends and the total length are both minimized. Although a smallest rectilinear path between two terminals in a rectilinear polygon always exists, they show that such a smallest pair may not exist for some problem instances. In that case, the algorithm presented will find, among all noncrossing paths with a minimum total number of bends, a pair whose total length is the shortest, or find, among all noncrossing paths with a minimum total length, a pair whose total number of bends is minimized. They provide a simple linear time and space algorithm based on the fact that there are only a limited number of configurations of such a solution pair.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/12.609280</doi><tpages>12</tpages></addata></record> |
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| ispartof | IEEE transactions on computers, 1997-08, Vol.46 (8), p.930-941 |
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| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Computational geometry Cost function Design. Technologies. Operation analysis. Testing Electronics Exact sciences and technology Integrated circuits Joining processes Motion planning Packaging Path planning Production facilities Robot motion Routing Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices Very large scale integration |
| title | The smallest pair of noncrossing paths in a rectilinear polygon |
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