On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique
We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique. Recently, primal-dual algorithms were devised by first constructing a local ratio algorithm and then transforming it int...
Gespeichert in:
| Veröffentlicht in: | SIAM journal on discrete mathematics 2005-01, Vol.19 (3), p.762-797 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 797 |
|---|---|
| container_issue | 3 |
| container_start_page | 762 |
| container_title | SIAM journal on discrete mathematics |
| container_volume | 19 |
| creator | Bar-Yehuda, Reuven Rawitz, Dror |
| description | We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique. Recently, primal-dual algorithms were devised by first constructing a local ratio algorithm and then transforming it into a primal-dual algorithm. This was done in the case of the $2$-approximation algorithms for the feedback vertex set problem and in the case of the first primal-dual algorithms for maximization problems. Subsequently, the nature of the connection between the two paradigms was posed as an open question by Williamson [Math. Program., 91 (2002), pp. 447--478]. In this paper we answer this question by showing that the two paradigms are equivalent. |
| doi_str_mv | 10.1137/050625382 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_925644863</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2599585051</sourcerecordid><originalsourceid>FETCH-LOGICAL-c357t-bb0c5f4de8b517732621eb6a5fb505b3852c9b032806c80bfd24f6a87b5a8fa13</originalsourceid><addsrcrecordid>eNo9UE1Lw0AUXETBWj34D4I3D9G3H2-zPUptVQhUtJ7D7vYtSUmTNh-K_97UiKd5zBtmmGHsmsMd5zK5BwQtUBpxwiYcZhgnXOlTNgEz3MoAP2cXbbsF4EpxnLDVqoq6nKLFoS8-bUmVp8hR90U08q9NsbNl_NjbMnr3Oe1sZKvN7yut_UC-2a6oozX5vCoOPV2ys2DLlq7-cMo-lov1_DlOV08v84c09hKTLnYOPAa1IeOQJ4kUWnBy2mJwCOikQeFnDqQwoL0BFzZCBW1N4tCaYLmcspvRd9_UQ2zbZdu6b6ohMpsJ1EoZLQfR7SjyTd22DYVsf6zTfGccsuNc2f9c8gcUqlrc</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>925644863</pqid></control><display><type>article</type><title>On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique</title><source>LOCUS - SIAM's Online Journal Archive</source><creator>Bar-Yehuda, Reuven ; Rawitz, Dror</creator><creatorcontrib>Bar-Yehuda, Reuven ; Rawitz, Dror</creatorcontrib><description>We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique. Recently, primal-dual algorithms were devised by first constructing a local ratio algorithm and then transforming it into a primal-dual algorithm. This was done in the case of the $2$-approximation algorithms for the feedback vertex set problem and in the case of the first primal-dual algorithms for maximization problems. Subsequently, the nature of the connection between the two paradigms was posed as an open question by Williamson [Math. Program., 91 (2002), pp. 447--478]. In this paper we answer this question by showing that the two paradigms are equivalent.</description><identifier>ISSN: 0895-4801</identifier><identifier>EISSN: 1095-7146</identifier><identifier>DOI: 10.1137/050625382</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><subject>Algorithms ; Approximation ; Computer science ; Integer programming ; Linear programming ; Optimization</subject><ispartof>SIAM journal on discrete mathematics, 2005-01, Vol.19 (3), p.762-797</ispartof><rights>[Copyright] © 2005 Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c357t-bb0c5f4de8b517732621eb6a5fb505b3852c9b032806c80bfd24f6a87b5a8fa13</citedby><cites>FETCH-LOGICAL-c357t-bb0c5f4de8b517732621eb6a5fb505b3852c9b032806c80bfd24f6a87b5a8fa13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,3184,27923,27924</link.rule.ids></links><search><creatorcontrib>Bar-Yehuda, Reuven</creatorcontrib><creatorcontrib>Rawitz, Dror</creatorcontrib><title>On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique</title><title>SIAM journal on discrete mathematics</title><description>We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique. Recently, primal-dual algorithms were devised by first constructing a local ratio algorithm and then transforming it into a primal-dual algorithm. This was done in the case of the $2$-approximation algorithms for the feedback vertex set problem and in the case of the first primal-dual algorithms for maximization problems. Subsequently, the nature of the connection between the two paradigms was posed as an open question by Williamson [Math. Program., 91 (2002), pp. 447--478]. In this paper we answer this question by showing that the two paradigms are equivalent.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Computer science</subject><subject>Integer programming</subject><subject>Linear programming</subject><subject>Optimization</subject><issn>0895-4801</issn><issn>1095-7146</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNo9UE1Lw0AUXETBWj34D4I3D9G3H2-zPUptVQhUtJ7D7vYtSUmTNh-K_97UiKd5zBtmmGHsmsMd5zK5BwQtUBpxwiYcZhgnXOlTNgEz3MoAP2cXbbsF4EpxnLDVqoq6nKLFoS8-bUmVp8hR90U08q9NsbNl_NjbMnr3Oe1sZKvN7yut_UC-2a6oozX5vCoOPV2ys2DLlq7-cMo-lov1_DlOV08v84c09hKTLnYOPAa1IeOQJ4kUWnBy2mJwCOikQeFnDqQwoL0BFzZCBW1N4tCaYLmcspvRd9_UQ2zbZdu6b6ohMpsJ1EoZLQfR7SjyTd22DYVsf6zTfGccsuNc2f9c8gcUqlrc</recordid><startdate>200501</startdate><enddate>200501</enddate><creator>Bar-Yehuda, Reuven</creator><creator>Rawitz, Dror</creator><general>Society for Industrial and Applied Mathematics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7X2</scope><scope>7XB</scope><scope>87Z</scope><scope>88A</scope><scope>88F</scope><scope>88I</scope><scope>88K</scope><scope>8AL</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KB.</scope><scope>L.-</scope><scope>L6V</scope><scope>LK8</scope><scope>M0C</scope><scope>M0K</scope><scope>M0N</scope><scope>M1Q</scope><scope>M2O</scope><scope>M2P</scope><scope>M2T</scope><scope>M7P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PDBOC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope></search><sort><creationdate>200501</creationdate><title>On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique</title><author>Bar-Yehuda, Reuven ; Rawitz, Dror</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c357t-bb0c5f4de8b517732621eb6a5fb505b3852c9b032806c80bfd24f6a87b5a8fa13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Algorithms</topic><topic>Approximation</topic><topic>Computer science</topic><topic>Integer programming</topic><topic>Linear programming</topic><topic>Optimization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bar-Yehuda, Reuven</creatorcontrib><creatorcontrib>Rawitz, Dror</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>Agricultural Science Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Military Database (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Telecommunications (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>Agricultural & Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Materials Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>ABI/INFORM Global</collection><collection>Agricultural Science Database</collection><collection>Computing Database</collection><collection>Military Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Telecommunications Database</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Materials Science Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><jtitle>SIAM journal on discrete mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bar-Yehuda, Reuven</au><au>Rawitz, Dror</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique</atitle><jtitle>SIAM journal on discrete mathematics</jtitle><date>2005-01</date><risdate>2005</risdate><volume>19</volume><issue>3</issue><spage>762</spage><epage>797</epage><pages>762-797</pages><issn>0895-4801</issn><eissn>1095-7146</eissn><abstract>We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique. Recently, primal-dual algorithms were devised by first constructing a local ratio algorithm and then transforming it into a primal-dual algorithm. This was done in the case of the $2$-approximation algorithms for the feedback vertex set problem and in the case of the first primal-dual algorithms for maximization problems. Subsequently, the nature of the connection between the two paradigms was posed as an open question by Williamson [Math. Program., 91 (2002), pp. 447--478]. In this paper we answer this question by showing that the two paradigms are equivalent.</abstract><cop>Philadelphia</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/050625382</doi><tpages>36</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0895-4801 |
| ispartof | SIAM journal on discrete mathematics, 2005-01, Vol.19 (3), p.762-797 |
| issn | 0895-4801 1095-7146 |
| language | eng |
| recordid | cdi_proquest_journals_925644863 |
| source | LOCUS - SIAM's Online Journal Archive |
| subjects | Algorithms Approximation Computer science Integer programming Linear programming Optimization |
| title | On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T19%3A00%3A28IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20Equivalence%20between%20the%20Primal-Dual%20Schema%20and%20the%20Local%20Ratio%20Technique&rft.jtitle=SIAM%20journal%20on%20discrete%20mathematics&rft.au=Bar-Yehuda,%20Reuven&rft.date=2005-01&rft.volume=19&rft.issue=3&rft.spage=762&rft.epage=797&rft.pages=762-797&rft.issn=0895-4801&rft.eissn=1095-7146&rft_id=info:doi/10.1137/050625382&rft_dat=%3Cproquest_cross%3E2599585051%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=925644863&rft_id=info:pmid/&rfr_iscdi=true |