Algorithm for K Disjoint Maximum Subarrays
The maximum subarray problem is to find the array portion that maximizes the sum of array elements in it. For K disjoint maximum subarrays, Ruzzo and Tompa gave an O(n) time solution for one-dimension. This solution is, however, difficult to extend to two-dimensions. While a trivial solution of O(Kn...
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| creator | Bae, Sung Eun Takaoka, Tadao |
| description | The maximum subarray problem is to find the array portion that maximizes the sum of array elements in it. For K disjoint maximum subarrays, Ruzzo and Tompa gave an O(n) time solution for one-dimension. This solution is, however, difficult to extend to two-dimensions. While a trivial solution of O(Kn3) time is easily obtainable for two-dimensions, little study has been undertaken to better this. We first propose an O(n+Klog K) time solution for one-dimension. This is equivalent to Ruzzo and Tompa’s when order is considered. Based on this, we achieve O(n3+Kn2log n) time for two-dimensions. This is cubic time when K≤ n/log n. |
| doi_str_mv | 10.1007/11758501_80 |
| format | Book Chapter |
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A.</contributor><creatorcontrib>Bae, Sung Eun ; Takaoka, Tadao ; Alexandrov, Vassil N. ; Dongarra, Jack ; van Albada, Geert Dick ; Sloot, Peter M. A.</creatorcontrib><description>The maximum subarray problem is to find the array portion that maximizes the sum of array elements in it. For K disjoint maximum subarrays, Ruzzo and Tompa gave an O(n) time solution for one-dimension. This solution is, however, difficult to extend to two-dimensions. While a trivial solution of O(Kn3) time is easily obtainable for two-dimensions, little study has been undertaken to better this. We first propose an O(n+Klog K) time solution for one-dimension. This is equivalent to Ruzzo and Tompa’s when order is considered. Based on this, we achieve O(n3+Kn2log n) time for two-dimensions. This is cubic time when K≤ n/log n.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 3540343792</identifier><identifier>ISBN: 9783540343790</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540343806</identifier><identifier>EISBN: 3540343806</identifier><identifier>DOI: 10.1007/11758501_80</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algorithmics. Computability. Computer arithmetics ; Applied sciences ; Array Element ; Computer science; control theory; systems ; Exact sciences and technology ; Input Array ; Small Physical Size ; Theoretical computing ; Time Solution ; Trivial Solution</subject><ispartof>Computational Science – ICCS 2006, 2006, p.595-602</ispartof><rights>Springer-Verlag Berlin Heidelberg 2006</rights><rights>2008 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/11758501_80$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/11758501_80$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,776,777,781,786,787,790,4036,4037,27906,38236,41423,42492</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19969020$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Alexandrov, Vassil N.</contributor><contributor>Dongarra, Jack</contributor><contributor>van Albada, Geert Dick</contributor><contributor>Sloot, Peter M. A.</contributor><creatorcontrib>Bae, Sung Eun</creatorcontrib><creatorcontrib>Takaoka, Tadao</creatorcontrib><title>Algorithm for K Disjoint Maximum Subarrays</title><title>Computational Science – ICCS 2006</title><description>The maximum subarray problem is to find the array portion that maximizes the sum of array elements in it. For K disjoint maximum subarrays, Ruzzo and Tompa gave an O(n) time solution for one-dimension. This solution is, however, difficult to extend to two-dimensions. While a trivial solution of O(Kn3) time is easily obtainable for two-dimensions, little study has been undertaken to better this. We first propose an O(n+Klog K) time solution for one-dimension. This is equivalent to Ruzzo and Tompa’s when order is considered. Based on this, we achieve O(n3+Kn2log n) time for two-dimensions. This is cubic time when K≤ n/log n.</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Applied sciences</subject><subject>Array Element</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Input Array</subject><subject>Small Physical Size</subject><subject>Theoretical computing</subject><subject>Time Solution</subject><subject>Trivial Solution</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>3540343792</isbn><isbn>9783540343790</isbn><isbn>9783540343806</isbn><isbn>3540343806</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2006</creationdate><recordtype>book_chapter</recordtype><recordid>eNpNkLtOw0AURJeXRAip-AE3FCAZ7t27zzIKTxFEAdSrtb0ODnEc7SYS-XuMkoJpppij0WgYu0C4QQB9i6ilkYDOwAEbWW1ICiBBBtQhG6BCzImEPWJn-0BbfswGQMBzqwWdslFKc-hFqAzaAbseL2ZdbNZfbVZ3MXvJ7po075rlOnv1P027abP3TeFj9Nt0zk5qv0hhtPch-3y4_5g85dO3x-fJeJqvuFTrXGnSnIMQ0tRVv6LgYGoKlQUy0hZacAgaghRBhQoKIFko7q2nIJBCWdOQXe56Vz6VflFHvyyb5FaxaX3cOrRWWeDQc1c7LvXRchaiK7ruOzkE93eW-3cW_QK9tlP_</recordid><startdate>2006</startdate><enddate>2006</enddate><creator>Bae, Sung Eun</creator><creator>Takaoka, Tadao</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>IQODW</scope></search><sort><creationdate>2006</creationdate><title>Algorithm for K Disjoint Maximum Subarrays</title><author>Bae, Sung Eun ; Takaoka, Tadao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p256t-67372204458fd540b208f3ed903859b7420e70e54e6ed0b035b62a9a3e413ecf3</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Algorithmics. Computability. Computer arithmetics</topic><topic>Applied sciences</topic><topic>Array Element</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Input Array</topic><topic>Small Physical Size</topic><topic>Theoretical computing</topic><topic>Time Solution</topic><topic>Trivial Solution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bae, Sung Eun</creatorcontrib><creatorcontrib>Takaoka, Tadao</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bae, Sung Eun</au><au>Takaoka, Tadao</au><au>Alexandrov, Vassil N.</au><au>Dongarra, Jack</au><au>van Albada, Geert Dick</au><au>Sloot, Peter M. A.</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Algorithm for K Disjoint Maximum Subarrays</atitle><btitle>Computational Science – ICCS 2006</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2006</date><risdate>2006</risdate><spage>595</spage><epage>602</epage><pages>595-602</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>3540343792</isbn><isbn>9783540343790</isbn><eisbn>9783540343806</eisbn><eisbn>3540343806</eisbn><abstract>The maximum subarray problem is to find the array portion that maximizes the sum of array elements in it. For K disjoint maximum subarrays, Ruzzo and Tompa gave an O(n) time solution for one-dimension. This solution is, however, difficult to extend to two-dimensions. While a trivial solution of O(Kn3) time is easily obtainable for two-dimensions, little study has been undertaken to better this. We first propose an O(n+Klog K) time solution for one-dimension. This is equivalent to Ruzzo and Tompa’s when order is considered. Based on this, we achieve O(n3+Kn2log n) time for two-dimensions. This is cubic time when K≤ n/log n.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/11758501_80</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Computational Science – ICCS 2006, 2006, p.595-602 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_19969020 |
| source | Springer Books |
| subjects | Algorithmics. Computability. Computer arithmetics Applied sciences Array Element Computer science control theory systems Exact sciences and technology Input Array Small Physical Size Theoretical computing Time Solution Trivial Solution |
| title | Algorithm for K Disjoint Maximum Subarrays |
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