Smaller Kernels for Hitting Set Problems of Constant Arity
We demonstrate a kernel of size O(k2) for 3-Hitting Set (Hitting Set when all subsets in the collection to be hit are of size at most three), giving a partial answer to an open question of Niedermeier by improving on the O(k3) kernel of Niedermeier and Rossmanith. Our technique uses the Nemhauser-Tr...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buchkapitel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 126 |
|---|---|
| container_issue | |
| container_start_page | 121 |
| container_title | |
| container_volume | 3162 |
| creator | Nishimura, Naomi Ragde, Prabhakar Thilikos, Dimitrios M. |
| description | We demonstrate a kernel of size O(k2) for 3-Hitting Set (Hitting Set when all subsets in the collection to be hit are of size at most three), giving a partial answer to an open question of Niedermeier by improving on the O(k3) kernel of Niedermeier and Rossmanith. Our technique uses the Nemhauser-Trotter linear-size kernel for Vertex Cover, and generalizes to demonstrating a kernel of size O(kr − − 1) for r-Hitting Set (for fixed r). |
| doi_str_mv | 10.1007/978-3-540-28639-4_11 |
| format | Book Chapter |
| fullrecord | <record><control><sourceid>proquest_pasca</sourceid><recordid>TN_cdi_pascalfrancis_primary_16194834</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>EBC3088602_17_128</sourcerecordid><originalsourceid>FETCH-LOGICAL-p272t-96f8fac13565fd5caa83a3f51b21055a21139f8fb6ff7618dce9a0422b0ee3843</originalsourceid><addsrcrecordid>eNpFkLtOwzAUhs1VRKVvwJCF0eDjk8Q2G6qAIiqBVJgtJ7VLIE2KbYa-Pe5F4ixH-m_DR8gVsBtgTNwqISnSsmCUywoVLTTAERknGZO404pjkkEFQBELdfLvIRMgTknGkHGqRIHnJFMpIpng4oKMQ_hi6TiIZGbkbr4yXWd9_mJ9b7uQu8Hn0zbGtl_mcxvzNz_UnV2FfHD5ZOhDNH3M730bN5fkzJku2PHhj8jH48P7ZEpnr0_Pk_sZXXPBI1WVk840gGVVukXZGCPRoCuh5sDK0nAAVClSV86JCuSiscqwgvOaWYuywBG53u-uTWhM57zpmzbotW9Xxm90gqAKidsc3-dCsvql9boehu-ggektVJ0IadSJkd4B1FuoqYSHcT_8_NoQtd22GttHb7rm06yj9UEjk7JiXIPQwCX-AbI_c28</addsrcrecordid><sourcetype>Index Database</sourcetype><iscdi>true</iscdi><recordtype>book_chapter</recordtype><pqid>EBC3088602_17_128</pqid></control><display><type>book_chapter</type><title>Smaller Kernels for Hitting Set Problems of Constant Arity</title><source>Springer Books</source><creator>Nishimura, Naomi ; Ragde, Prabhakar ; Thilikos, Dimitrios M.</creator><contributor>Dehne, Frank ; Downey, Rod ; Fellows, Michael ; Dehne, Frank ; Downey, Rod ; Fellows, Michael</contributor><creatorcontrib>Nishimura, Naomi ; Ragde, Prabhakar ; Thilikos, Dimitrios M. ; Dehne, Frank ; Downey, Rod ; Fellows, Michael ; Dehne, Frank ; Downey, Rod ; Fellows, Michael</creatorcontrib><description>We demonstrate a kernel of size O(k2) for 3-Hitting Set (Hitting Set when all subsets in the collection to be hit are of size at most three), giving a partial answer to an open question of Niedermeier by improving on the O(k3) kernel of Niedermeier and Rossmanith. Our technique uses the Nemhauser-Trotter linear-size kernel for Vertex Cover, and generalizes to demonstrating a kernel of size O(kr − − 1) for r-Hitting Set (for fixed r).</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540230717</identifier><identifier>ISBN: 3540230718</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540286394</identifier><identifier>EISBN: 354028639X</identifier><identifier>DOI: 10.1007/978-3-540-28639-4_11</identifier><identifier>OCLC: 934980727</identifier><identifier>LCCallNum: QA76.9.A43</identifier><language>eng</language><publisher>Germany: Springer Berlin / Heidelberg</publisher><subject>Algorithmics. Computability. Computer arithmetics ; Applied sciences ; Computer science; control theory; systems ; Exact sciences and technology ; fixed parameter algorithms ; hitting set ; kernels ; Theoretical computing</subject><ispartof>Lecture notes in computer science, 2004, Vol.3162, p.121-126</ispartof><rights>Springer-Verlag Berlin Heidelberg 2004</rights><rights>2004 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttps://ebookcentral.proquest.com/covers/3088602-l.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/978-3-540-28639-4_11$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/978-3-540-28639-4_11$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,775,776,780,785,786,789,4036,4037,27904,38234,41421,42490</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16194834$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Dehne, Frank</contributor><contributor>Downey, Rod</contributor><contributor>Fellows, Michael</contributor><contributor>Dehne, Frank</contributor><contributor>Downey, Rod</contributor><contributor>Fellows, Michael</contributor><creatorcontrib>Nishimura, Naomi</creatorcontrib><creatorcontrib>Ragde, Prabhakar</creatorcontrib><creatorcontrib>Thilikos, Dimitrios M.</creatorcontrib><title>Smaller Kernels for Hitting Set Problems of Constant Arity</title><title>Lecture notes in computer science</title><description>We demonstrate a kernel of size O(k2) for 3-Hitting Set (Hitting Set when all subsets in the collection to be hit are of size at most three), giving a partial answer to an open question of Niedermeier by improving on the O(k3) kernel of Niedermeier and Rossmanith. Our technique uses the Nemhauser-Trotter linear-size kernel for Vertex Cover, and generalizes to demonstrating a kernel of size O(kr − − 1) for r-Hitting Set (for fixed r).</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>fixed parameter algorithms</subject><subject>hitting set</subject><subject>kernels</subject><subject>Theoretical computing</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540230717</isbn><isbn>3540230718</isbn><isbn>9783540286394</isbn><isbn>354028639X</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2004</creationdate><recordtype>book_chapter</recordtype><recordid>eNpFkLtOwzAUhs1VRKVvwJCF0eDjk8Q2G6qAIiqBVJgtJ7VLIE2KbYa-Pe5F4ixH-m_DR8gVsBtgTNwqISnSsmCUywoVLTTAERknGZO404pjkkEFQBELdfLvIRMgTknGkHGqRIHnJFMpIpng4oKMQ_hi6TiIZGbkbr4yXWd9_mJ9b7uQu8Hn0zbGtl_mcxvzNz_UnV2FfHD5ZOhDNH3M730bN5fkzJku2PHhj8jH48P7ZEpnr0_Pk_sZXXPBI1WVk840gGVVukXZGCPRoCuh5sDK0nAAVClSV86JCuSiscqwgvOaWYuywBG53u-uTWhM57zpmzbotW9Xxm90gqAKidsc3-dCsvql9boehu-ggektVJ0IadSJkd4B1FuoqYSHcT_8_NoQtd22GttHb7rm06yj9UEjk7JiXIPQwCX-AbI_c28</recordid><startdate>2004</startdate><enddate>2004</enddate><creator>Nishimura, Naomi</creator><creator>Ragde, Prabhakar</creator><creator>Thilikos, Dimitrios M.</creator><general>Springer Berlin / Heidelberg</general><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>FFUUA</scope><scope>IQODW</scope></search><sort><creationdate>2004</creationdate><title>Smaller Kernels for Hitting Set Problems of Constant Arity</title><author>Nishimura, Naomi ; Ragde, Prabhakar ; Thilikos, Dimitrios M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p272t-96f8fac13565fd5caa83a3f51b21055a21139f8fb6ff7618dce9a0422b0ee3843</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Algorithmics. Computability. Computer arithmetics</topic><topic>Applied sciences</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>fixed parameter algorithms</topic><topic>hitting set</topic><topic>kernels</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nishimura, Naomi</creatorcontrib><creatorcontrib>Ragde, Prabhakar</creatorcontrib><creatorcontrib>Thilikos, Dimitrios M.</creatorcontrib><collection>ProQuest Ebook Central - Book Chapters - Demo use only</collection><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nishimura, Naomi</au><au>Ragde, Prabhakar</au><au>Thilikos, Dimitrios M.</au><au>Dehne, Frank</au><au>Downey, Rod</au><au>Fellows, Michael</au><au>Dehne, Frank</au><au>Downey, Rod</au><au>Fellows, Michael</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Smaller Kernels for Hitting Set Problems of Constant Arity</atitle><btitle>Lecture notes in computer science</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2004</date><risdate>2004</risdate><volume>3162</volume><spage>121</spage><epage>126</epage><pages>121-126</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540230717</isbn><isbn>3540230718</isbn><eisbn>9783540286394</eisbn><eisbn>354028639X</eisbn><abstract>We demonstrate a kernel of size O(k2) for 3-Hitting Set (Hitting Set when all subsets in the collection to be hit are of size at most three), giving a partial answer to an open question of Niedermeier by improving on the O(k3) kernel of Niedermeier and Rossmanith. Our technique uses the Nemhauser-Trotter linear-size kernel for Vertex Cover, and generalizes to demonstrating a kernel of size O(kr − − 1) for r-Hitting Set (for fixed r).</abstract><cop>Germany</cop><pub>Springer Berlin / Heidelberg</pub><doi>10.1007/978-3-540-28639-4_11</doi><oclcid>934980727</oclcid><tpages>6</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Lecture notes in computer science, 2004, Vol.3162, p.121-126 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_16194834 |
| source | Springer Books |
| subjects | Algorithmics. Computability. Computer arithmetics Applied sciences Computer science control theory systems Exact sciences and technology fixed parameter algorithms hitting set kernels Theoretical computing |
| title | Smaller Kernels for Hitting Set Problems of Constant Arity |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-27T22%3A40%3A28IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_pasca&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=bookitem&rft.atitle=Smaller%20Kernels%20for%20Hitting%20Set%20Problems%20of%20Constant%20Arity&rft.btitle=Lecture%20notes%20in%20computer%20science&rft.au=Nishimura,%20Naomi&rft.date=2004&rft.volume=3162&rft.spage=121&rft.epage=126&rft.pages=121-126&rft.issn=0302-9743&rft.eissn=1611-3349&rft.isbn=9783540230717&rft.isbn_list=3540230718&rft_id=info:doi/10.1007/978-3-540-28639-4_11&rft_dat=%3Cproquest_pasca%3EEBC3088602_17_128%3C/proquest_pasca%3E%3Curl%3E%3C/url%3E&rft.eisbn=9783540286394&rft.eisbn_list=354028639X&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=EBC3088602_17_128&rft_id=info:pmid/&rfr_iscdi=true |