How to Trim an MST: A 2-Approximation Algorithm for Minimum Cost Tree Cover
The minimum cost tree cover problem is to compute a minimum cost tree T in a given connected graph G with costs on the edges, such that the vertices of T form a vertex cover for G. The problem is supposed to arise in applications of vertex cover and edge dominating set when connectivity is additiona...
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| creator | Fujito, Toshihiro |
| description | The minimum cost tree cover problem is to compute a minimum cost tree T in a given connected graph G with costs on the edges, such that the vertices of T form a vertex cover for G. The problem is supposed to arise in applications of vertex cover and edge dominating set when connectivity is additionally required in solutions. Whereas a linear-time 2-approximation algorithm for the unweighted case has been known for quite a while, the best approximation ratio known for the weighted case is 3. Moreover, the known 3-approximation algorithm for such case is far from practical in its efficiency.
In this paper we present a fast, purely combinatorial 2-approximation algorithm for the minimum cost tree cover problem. It constructs a good approximate solution by trimming some leaves within a minimum spanning tree (MST), and to determine which leaves to trim, it uses both of the primal-dual schema and the local ratio technique in an interlaced fashion. |
| doi_str_mv | 10.1007/11786986_38 |
| format | Conference Proceeding |
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In this paper we present a fast, purely combinatorial 2-approximation algorithm for the minimum cost tree cover problem. It constructs a good approximate solution by trimming some leaves within a minimum spanning tree (MST), and to determine which leaves to trim, it uses both of the primal-dual schema and the local ratio technique in an interlaced fashion.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 3540359044</identifier><identifier>ISBN: 9783540359043</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 3540359052</identifier><identifier>EISBN: 9783540359050</identifier><identifier>DOI: 10.1007/11786986_38</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied sciences ; Automata. Abstract machines. Turing machines ; Computer science; control theory; systems ; Exact sciences and technology ; Theoretical computing</subject><ispartof>Automata, Languages and Programming, 2006, p.431-442</ispartof><rights>Springer-Verlag Berlin Heidelberg 2006</rights><rights>2008 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c327t-fea3b6a6265a8a99e7709cae0cc9c414421e722c82cbdebc9bf8995234afce6b3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/11786986_38$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/11786986_38$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,779,780,784,789,790,793,4050,4051,27925,38255,41442,42511</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19993443$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Preneel, Bart</contributor><contributor>Bugliesi, Michele</contributor><contributor>Wegener, Ingo</contributor><contributor>Sassone, Vladimiro</contributor><creatorcontrib>Fujito, Toshihiro</creatorcontrib><title>How to Trim an MST: A 2-Approximation Algorithm for Minimum Cost Tree Cover</title><title>Automata, Languages and Programming</title><description>The minimum cost tree cover problem is to compute a minimum cost tree T in a given connected graph G with costs on the edges, such that the vertices of T form a vertex cover for G. The problem is supposed to arise in applications of vertex cover and edge dominating set when connectivity is additionally required in solutions. Whereas a linear-time 2-approximation algorithm for the unweighted case has been known for quite a while, the best approximation ratio known for the weighted case is 3. Moreover, the known 3-approximation algorithm for such case is far from practical in its efficiency.
In this paper we present a fast, purely combinatorial 2-approximation algorithm for the minimum cost tree cover problem. It constructs a good approximate solution by trimming some leaves within a minimum spanning tree (MST), and to determine which leaves to trim, it uses both of the primal-dual schema and the local ratio technique in an interlaced fashion.</description><subject>Applied sciences</subject><subject>Automata. Abstract machines. Turing machines</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Theoretical computing</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>3540359044</isbn><isbn>9783540359043</isbn><isbn>3540359052</isbn><isbn>9783540359050</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2006</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNpNkEtPwzAQhM1LIpSe-AO-cOAQsL2Ok-UWVUARrThQzpZjnBJo4sgOr39PUJFgL7PSfLvSDCEnnJ1zxvILzvNCYaE0FDvkCDLJIEOWiV2ScMV5CiBx78-Qcp8kDJhIMZdwSKYxvrBxgCtASMjd3H_QwdNVaFpqOrp8WF3Skoq07PvgP5vWDI3vaLlZ-9AMzy2tfaDLpmvat5bOfBzGS-fG7d2FY3JQm01001-dkMfrq9Vsni7ub25n5SK1IPIhrZ2BShklVGYKg-jynKE1jlmLVnIpBXe5ELYQtnpylcWqLhAzAdLU1qkKJuR0-7c30ZpNHUxnm6j7MYIJX5ojIkgJI3e25eJodWsXdOX9a9Sc6Z8q9b8q4RsfE1_C</recordid><startdate>2006</startdate><enddate>2006</enddate><creator>Fujito, Toshihiro</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>IQODW</scope></search><sort><creationdate>2006</creationdate><title>How to Trim an MST: A 2-Approximation Algorithm for Minimum Cost Tree Cover</title><author>Fujito, Toshihiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c327t-fea3b6a6265a8a99e7709cae0cc9c414421e722c82cbdebc9bf8995234afce6b3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Applied sciences</topic><topic>Automata. Abstract machines. Turing machines</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fujito, Toshihiro</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fujito, Toshihiro</au><au>Preneel, Bart</au><au>Bugliesi, Michele</au><au>Wegener, Ingo</au><au>Sassone, Vladimiro</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>How to Trim an MST: A 2-Approximation Algorithm for Minimum Cost Tree Cover</atitle><btitle>Automata, Languages and Programming</btitle><date>2006</date><risdate>2006</risdate><spage>431</spage><epage>442</epage><pages>431-442</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>3540359044</isbn><isbn>9783540359043</isbn><eisbn>3540359052</eisbn><eisbn>9783540359050</eisbn><abstract>The minimum cost tree cover problem is to compute a minimum cost tree T in a given connected graph G with costs on the edges, such that the vertices of T form a vertex cover for G. The problem is supposed to arise in applications of vertex cover and edge dominating set when connectivity is additionally required in solutions. Whereas a linear-time 2-approximation algorithm for the unweighted case has been known for quite a while, the best approximation ratio known for the weighted case is 3. Moreover, the known 3-approximation algorithm for such case is far from practical in its efficiency.
In this paper we present a fast, purely combinatorial 2-approximation algorithm for the minimum cost tree cover problem. It constructs a good approximate solution by trimming some leaves within a minimum spanning tree (MST), and to determine which leaves to trim, it uses both of the primal-dual schema and the local ratio technique in an interlaced fashion.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/11786986_38</doi><tpages>12</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Automata, Languages and Programming, 2006, p.431-442 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_19993443 |
| source | Springer Books |
| subjects | Applied sciences Automata. Abstract machines. Turing machines Computer science control theory systems Exact sciences and technology Theoretical computing |
| title | How to Trim an MST: A 2-Approximation Algorithm for Minimum Cost Tree Cover |
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