Rectilinear short path queries among rectangular obstacles
Given a set of n disjoint rectangular obstacles in the plane whose edges are either vertical or horizontal, we consider the problem of processing rectilinear approximate shortest path queries between pairs of arbitrary query points. Our goal is to answer each approximate shortest path query quickly...
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| Veröffentlicht in: | Information processing letters 1996-03, Vol.57 (6), p.313-319 |
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| container_title | Information processing letters |
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| creator | Chen, Danny A. Klenk, Kevin S. |
| description | Given a set of
n disjoint rectangular obstacles in the plane whose edges are either vertical or horizontal, we consider the problem of processing rectilinear approximate shortest path queries between pairs of arbitrary query points. Our goal is to answer each approximate shortest path query quickly by constructing a data structure that captures path information in the obstacle-scattered plane. We present a data structure for rectilinear approximate shortest path queries that requires O(
n
log
2
n) time to construct and O(
n
log
n) space. This data structure enables us to report the length of an approximate shortest path between two arbitrary query points in O(
log
n) time and the actual path in O(
log
n +
L) time, where
L is the number of edges of the output path. If the query points are both obstacle vertices then the length and an actual path can be reported in O(1) and O(
L) time respectively. The approximation factor for the approximate shortest paths that we compute is 3. The previously best known solution to this problem requires O(
n
log
3
n) time and O(
n
log
2
n) space to build a data structure, which supports length and actual path queries respectively in O(
log
2
n) and O(
log
2
n +
L) time (regardless of the types of query points); the approximation factor for paths between arbitrary query points is 7. |
| doi_str_mv | 10.1016/0020-0190(96)00020-8 |
| format | Article |
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n disjoint rectangular obstacles in the plane whose edges are either vertical or horizontal, we consider the problem of processing rectilinear approximate shortest path queries between pairs of arbitrary query points. Our goal is to answer each approximate shortest path query quickly by constructing a data structure that captures path information in the obstacle-scattered plane. We present a data structure for rectilinear approximate shortest path queries that requires O(
n
log
2
n) time to construct and O(
n
log
n) space. This data structure enables us to report the length of an approximate shortest path between two arbitrary query points in O(
log
n) time and the actual path in O(
log
n +
L) time, where
L is the number of edges of the output path. If the query points are both obstacle vertices then the length and an actual path can be reported in O(1) and O(
L) time respectively. The approximation factor for the approximate shortest paths that we compute is 3. The previously best known solution to this problem requires O(
n
log
3
n) time and O(
n
log
2
n) space to build a data structure, which supports length and actual path queries respectively in O(
log
2
n) and O(
log
2
n +
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n disjoint rectangular obstacles in the plane whose edges are either vertical or horizontal, we consider the problem of processing rectilinear approximate shortest path queries between pairs of arbitrary query points. Our goal is to answer each approximate shortest path query quickly by constructing a data structure that captures path information in the obstacle-scattered plane. We present a data structure for rectilinear approximate shortest path queries that requires O(
n
log
2
n) time to construct and O(
n
log
n) space. This data structure enables us to report the length of an approximate shortest path between two arbitrary query points in O(
log
n) time and the actual path in O(
log
n +
L) time, where
L is the number of edges of the output path. If the query points are both obstacle vertices then the length and an actual path can be reported in O(1) and O(
L) time respectively. The approximation factor for the approximate shortest paths that we compute is 3. The previously best known solution to this problem requires O(
n
log
3
n) time and O(
n
log
2
n) space to build a data structure, which supports length and actual path queries respectively in O(
log
2
n) and O(
log
2
n +
L) time (regardless of the types of query points); the approximation factor for paths between arbitrary query points is 7.</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Algorithms</subject><subject>Analysis of algorithms</subject><subject>Applied sciences</subject><subject>Artificial intelligence</subject><subject>Computational geometry</subject><subject>Computer science</subject><subject>Computer science; control theory; systems</subject><subject>Data processing. List processing. Character string processing</subject><subject>Data structures</subject><subject>Design of algorithms</subject><subject>Exact sciences and technology</subject><subject>Graphs</subject><subject>Mathematical models</subject><subject>Memory organisation. Data processing</subject><subject>Pattern recognition. Digital image processing. Computational geometry</subject><subject>Queries</subject><subject>Shortest path</subject><subject>Software</subject><subject>Studies</subject><subject>Systems design</subject><subject>Theoretical computing</subject><issn>0020-0190</issn><issn>1872-6119</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1996</creationdate><recordtype>article</recordtype><recordid>eNp9kM1Lw0AQxRdRsFb_Aw9BPOghOptN9sODUIpfUBBEz8tmM2m3pEndTQX_ezdt6dHT8OD33sw8Qi4p3FGg_B4ggxSoghvFb2Gr5BEZUSmylFOqjsnogJySsxCWEeI5EyPy8IG2d41r0fgkLDrfJ2vTL5LvDXqHITGrrp0nPkKmnW-aCHVl6I1tMJyTk9o0AS_2c0y-np8-p6_p7P3lbTqZpZZx6NMSDWcKi7yowZa0FqUEVliErGBYcVUJpqQUgqGqoCiUQlYqpFZKyfPK1GxMrna5a9_Fs0Kvl93Gt3GlzpjIhKCMRyjfQdZ3IXis9dq7lfG_moIeStJDA3poQKtBDEpG2_U-2wRrmtqb1rpw8DLglG_TH3cYxj9_HHodrMPWYuWGanTVuf_3_AFLRHmZ</recordid><startdate>19960325</startdate><enddate>19960325</enddate><creator>Chen, Danny A.</creator><creator>Klenk, Kevin S.</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>19960325</creationdate><title>Rectilinear short path queries among rectangular obstacles</title><author>Chen, Danny A. ; Klenk, Kevin S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-bea639e545f0cb1f7b8035ce0253ed69d73988773e9d05599e3b9e1c88864daf3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1996</creationdate><topic>Algorithmics. Computability. Computer arithmetics</topic><topic>Algorithms</topic><topic>Analysis of algorithms</topic><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Computational geometry</topic><topic>Computer science</topic><topic>Computer science; control theory; systems</topic><topic>Data processing. List processing. Character string processing</topic><topic>Data structures</topic><topic>Design of algorithms</topic><topic>Exact sciences and technology</topic><topic>Graphs</topic><topic>Mathematical models</topic><topic>Memory organisation. Data processing</topic><topic>Pattern recognition. Digital image processing. Computational geometry</topic><topic>Queries</topic><topic>Shortest path</topic><topic>Software</topic><topic>Studies</topic><topic>Systems design</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Danny A.</creatorcontrib><creatorcontrib>Klenk, Kevin S.</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>Chen, Danny A.</au><au>Klenk, Kevin S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Rectilinear short path queries among rectangular obstacles</atitle><jtitle>Information processing letters</jtitle><date>1996-03-25</date><risdate>1996</risdate><volume>57</volume><issue>6</issue><spage>313</spage><epage>319</epage><pages>313-319</pages><issn>0020-0190</issn><eissn>1872-6119</eissn><coden>IFPLAT</coden><abstract>Given a set of
n disjoint rectangular obstacles in the plane whose edges are either vertical or horizontal, we consider the problem of processing rectilinear approximate shortest path queries between pairs of arbitrary query points. Our goal is to answer each approximate shortest path query quickly by constructing a data structure that captures path information in the obstacle-scattered plane. We present a data structure for rectilinear approximate shortest path queries that requires O(
n
log
2
n) time to construct and O(
n
log
n) space. This data structure enables us to report the length of an approximate shortest path between two arbitrary query points in O(
log
n) time and the actual path in O(
log
n +
L) time, where
L is the number of edges of the output path. If the query points are both obstacle vertices then the length and an actual path can be reported in O(1) and O(
L) time respectively. The approximation factor for the approximate shortest paths that we compute is 3. The previously best known solution to this problem requires O(
n
log
3
n) time and O(
n
log
2
n) space to build a data structure, which supports length and actual path queries respectively in O(
log
2
n) and O(
log
2
n +
L) time (regardless of the types of query points); the approximation factor for paths between arbitrary query points is 7.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/0020-0190(96)00020-8</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0020-0190 |
| ispartof | Information processing letters, 1996-03, Vol.57 (6), p.313-319 |
| issn | 0020-0190 1872-6119 |
| language | eng |
| recordid | cdi_proquest_journals_237277136 |
| source | Elsevier ScienceDirect Journals |
| subjects | Algorithmics. Computability. Computer arithmetics Algorithms Analysis of algorithms Applied sciences Artificial intelligence Computational geometry Computer science Computer science control theory systems Data processing. List processing. Character string processing Data structures Design of algorithms Exact sciences and technology Graphs Mathematical models Memory organisation. Data processing Pattern recognition. Digital image processing. Computational geometry Queries Shortest path Software Studies Systems design Theoretical computing |
| title | Rectilinear short path queries among rectangular obstacles |
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