<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00128750</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-19T02:43:11+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Longest Common Separable Pattern between Permutations</title>
            <author role="aut">
              <persName>
                <forename type="first">Mathilde</forename>
                <surname>Bouvel</surname>
              </persName>
              <email type="md5">58bd01fedc6af013578a841458c3f617</email>
              <email type="domain">loria.fr</email>
              <idno type="idhal" notation="string">mathildebouvel</idno>
              <idno type="idhal" notation="numeric">739190</idno>
              <idno type="halauthorid" notation="string">1270-739190</idno>
              <idno type="IDREF">https://www.idref.fr/142525995</idno>
              <affiliation ref="#struct-1033"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Dominique</forename>
                <surname>Rossin</surname>
              </persName>
              <email type="md5">351e1c31829350780314a8ec27cb0f2a</email>
              <email type="domain">polytechnique.org</email>
              <idno type="idhal" notation="string">dominique-rossin</idno>
              <idno type="idhal" notation="numeric">4815</idno>
              <idno type="halauthorid" notation="string">17556-4815</idno>
              <idno type="IDREF">https://www.idref.fr/142525707</idno>
              <affiliation ref="#struct-1033"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Stéphane</forename>
                <surname>Vialette</surname>
              </persName>
              <email type="md5">57f9bd64dbe2de8e92c394b5e7463974</email>
              <email type="domain">univ-eiffel.fr</email>
              <idno type="idhal" notation="string">stephane-vialette</idno>
              <idno type="idhal" notation="numeric">3062</idno>
              <idno type="halauthorid" notation="string">14060-3062</idno>
              <idno type="IDREF">https://www.idref.fr/061620734</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-2308-6970</idno>
              <orgName ref="#struct-441569"/>
              <affiliation ref="#struct-394095"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Mathilde</forename>
                <surname>Bouvel</surname>
              </persName>
              <email type="md5">58bd01fedc6af013578a841458c3f617</email>
              <email type="domain">loria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2007-02-05 17:18:29</date>
              <date type="whenModified">2024-12-09 15:38:02</date>
              <date type="whenReleased">2007-02-05 17:31:07</date>
              <date type="whenProduced">2007</date>
              <date type="whenEndEmbargoed">2007-02-05</date>
              <ref type="file" target="https://hal.science/hal-00128750v1/document">
                <date notBefore="2007-02-05"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00128750v1/file/LongestCommonSeparablePermutation.pdf" id="file-128750-1040750">
                <date notBefore="2007-02-05"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/math.CO/0702109"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="318880">
                <persName>
                  <forename>Mathilde</forename>
                  <surname>Bouvel</surname>
                </persName>
                <email type="md5">58bd01fedc6af013578a841458c3f617</email>
                <email type="domain">loria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00128750</idno>
            <idno type="halUri">https://hal.science/hal-00128750</idno>
            <idno type="halBibtex">bouvel:hal-00128750</idno>
            <idno type="halRefHtml">&lt;i&gt;Combinatorial Pattern Matching, 18th Annual Symposium, CPM 2007, London, Canada, July 9-11, 2007&lt;/i&gt;, 2007, London, Canada. pp.316-327</idno>
            <idno type="halRef">Combinatorial Pattern Matching, 18th Annual Symposium, CPM 2007, London, Canada, July 9-11, 2007, 2007, London, Canada. pp.316-327</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-128750-1040750"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-PARIS7" corresp="UNIV-PARIS">Université Denis Diderot - Paris VII</idno>
            <idno type="stamp" n="ENS-PARIS">Ecole Normale Supérieure de Paris</idno>
            <idno type="stamp" n="EC-PARIS">Ecole Centrale Paris</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-PSUD">Université Paris Sud - Paris XI</idno>
            <idno type="stamp" n="LIAFA">Laboratoire d'Informatique Algorithmique, Fondements et Applications</idno>
            <idno type="stamp" n="UMR8623">Laboratoire de Recherche en Informatique</idno>
            <idno type="stamp" n="PSL">Université Paris sciences et lettres</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="UNIV-PSUD-SACLAY" corresp="UNIV-PARIS-SACLAY">Université Paris Sud pour Paris Saclay</idno>
            <idno type="stamp" n="UNIV-PARIS">Université Paris Cité</idno>
            <idno type="stamp" n="ENS-PSL" corresp="PSL">École normale supérieure - PSL</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">15 pages</note>
            <note type="audience" n="2">International</note>
            <note type="invited" n="0">No</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
            <note type="proceedings" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Longest Common Separable Pattern between Permutations</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Mathilde</forename>
                    <surname>Bouvel</surname>
                  </persName>
                  <email type="md5">58bd01fedc6af013578a841458c3f617</email>
                  <email type="domain">loria.fr</email>
                  <idno type="idhal" notation="string">mathildebouvel</idno>
                  <idno type="idhal" notation="numeric">739190</idno>
                  <idno type="halauthorid" notation="string">1270-739190</idno>
                  <idno type="IDREF">https://www.idref.fr/142525995</idno>
                  <affiliation ref="#struct-1033"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Dominique</forename>
                    <surname>Rossin</surname>
                  </persName>
                  <email type="md5">351e1c31829350780314a8ec27cb0f2a</email>
                  <email type="domain">polytechnique.org</email>
                  <idno type="idhal" notation="string">dominique-rossin</idno>
                  <idno type="idhal" notation="numeric">4815</idno>
                  <idno type="halauthorid" notation="string">17556-4815</idno>
                  <idno type="IDREF">https://www.idref.fr/142525707</idno>
                  <affiliation ref="#struct-1033"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Stéphane</forename>
                    <surname>Vialette</surname>
                  </persName>
                  <email type="md5">57f9bd64dbe2de8e92c394b5e7463974</email>
                  <email type="domain">univ-eiffel.fr</email>
                  <idno type="idhal" notation="string">stephane-vialette</idno>
                  <idno type="idhal" notation="numeric">3062</idno>
                  <idno type="halauthorid" notation="string">14060-3062</idno>
                  <idno type="IDREF">https://www.idref.fr/061620734</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-2308-6970</idno>
                  <orgName ref="#struct-441569"/>
                  <affiliation ref="#struct-394095"/>
                </author>
              </analytic>
              <monogr>
                <title level="m">Combinatorial Pattern Matching (CPM) 2007, Proceedings</title>
                <meeting>
                  <title>Combinatorial Pattern Matching, 18th Annual Symposium, CPM 2007, London, Canada, July 9-11, 2007</title>
                  <date type="start">2007</date>
                  <settlement>London</settlement>
                  <country key="CA">Canada</country>
                </meeting>
                <editor>Bin Ma and Kaizhong Zhang</editor>
                <imprint>
                  <publisher>Springer</publisher>
                  <biblScope unit="serie">Lecture Notes in Computer Science (LNCS)</biblScope>
                  <biblScope unit="volume">4580</biblScope>
                  <biblScope unit="pp">316-327</biblScope>
                  <date type="datePub">2007</date>
                </imprint>
              </monogr>
              <idno type="arxiv">math.CO/0702109</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">permutation</term>
                <term xml:lang="en">pattern matching</term>
              </keywords>
              <classCode scheme="classification">05A05 - 05C12 - 05C85 - 05C05- 90C39</classCode>
              <classCode scheme="halDomain" n="math.math-co">Mathematics [math]/Combinatorics [math.CO]</classCode>
              <classCode scheme="halDomain" n="info.info-cc">Computer Science [cs]/Computational Complexity [cs.CC]</classCode>
              <classCode scheme="halTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halOldTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halTreeTypology" n="COMM">Conference papers</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this article, we study the problem of finding the longest common separable pattern between several permutations. We give a polynomial-time algorithm when the number of input permutations is fixed and show that the problem is NP-hard for an arbitrary number of input permutations even if these permutations are separable. On the other hand, we show that the NP-hard problem of finding the longest common pattern between two permutations cannot be approximated better than within a ratio of $sqrt{Opt}$ (where $Opt$ is the size of an optimal solution) when taking common patterns belonging to pattern-avoiding classes of permutations.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1033" status="OLD">
          <orgName>Laboratoire d'informatique Algorithmique : Fondements et Applications</orgName>
          <orgName type="acronym">LIAFA</orgName>
          <date type="start">1997-01-01</date>
          <date type="end">2015-12-31</date>
          <desc>
            <address>
              <addrLine>Université Paris Diderot, Bât. Sophie Germain, case postale 7014, 75205 Paris cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.liafa.jussieu.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300301" type="direct"/>
            <relation name="UMR7089" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-394095" status="OLD">
          <orgName>Algorithmics</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-1309" type="direct"/>
            <relation active="#struct-34292" type="indirect"/>
            <relation active="#struct-59704" type="indirect"/>
            <relation active="#struct-564132" type="indirect"/>
            <relation active="#struct-303623" type="indirect"/>
            <relation active="#struct-441569" type="indirect"/>
            <relation name="UMR8541" active="#struct-441569" type="indirect"/>
            <relation active="#struct-2544" type="direct"/>
            <relation active="#struct-92966" type="indirect"/>
            <relation active="#struct-411575" type="indirect"/>
            <relation name="UMR8623" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300301" status="OLD">
          <idno type="IdRef">027542084</idno>
          <idno type="ISNI">0000000121514068</idno>
          <idno type="ROR">https://ror.org/02n7qrg46</idno>
          <orgName>Université Paris Diderot - Paris 7</orgName>
          <orgName type="acronym">UPD7</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>5 rue Thomas-Mann - 75205 Paris cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-paris-diderot.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-1309" status="OLD">
          <idno type="RNSR">199812869B</idno>
          <orgName>Régulation de l'expression génétique</orgName>
          <orgName type="acronym">REG</orgName>
          <date type="start">1998</date>
          <date type="end">2009-12-31</date>
          <desc>
            <address>
              <addrLine>46 Rue d'Ulm 75230 PARIS CEDEX 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.biologie.ens.fr/lgm/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-34292" type="direct"/>
            <relation active="#struct-59704" type="indirect"/>
            <relation active="#struct-564132" type="indirect"/>
            <relation active="#struct-303623" type="indirect"/>
            <relation active="#struct-441569" type="direct"/>
            <relation name="UMR8541" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-34292" status="VALID">
          <orgName>Département de Biologie - ENS-PSL</orgName>
          <orgName type="acronym">IBENS</orgName>
          <date type="start">1987-01-01</date>
          <desc>
            <address>
              <addrLine>Département de BiologieENS Ulm46 rue d 'Ulm75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.biologie.ens.fr/depbio/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-59704" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
            <relation active="#struct-303623" type="direct"/>
            <relation active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-59704" status="VALID">
          <idno type="IdRef">031738419</idno>
          <idno type="ISNI">0000000123532622</idno>
          <idno type="ROR">https://ror.org/05a0dhs15</idno>
          <orgName>École normale supérieure - Paris</orgName>
          <orgName type="acronym">ENS-PSL</orgName>
          <date type="start">1985-07-24</date>
          <desc>
            <address>
              <addrLine>45, Rue d'Ulm - 75230 Paris cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ens.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-564132" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-564132" status="VALID">
          <idno type="IdRef">241597595</idno>
          <idno type="ISNI">0000 0004 1784 3645</idno>
          <idno type="ROR">https://ror.org/013cjyk83</idno>
          <orgName>Université Paris Sciences et Lettres</orgName>
          <orgName type="acronym">PSL</orgName>
          <desc>
            <address>
              <addrLine>60 rue Mazarine 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.psl.eu/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-303623" status="VALID">
          <idno type="IdRef">026388278</idno>
          <idno type="ROR">https://ror.org/02vjkv261</idno>
          <orgName>Institut National de la Santé et de la Recherche Médicale</orgName>
          <orgName type="acronym">INSERM</orgName>
          <desc>
            <address>
              <addrLine>101, rue de Tolbiac, 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inserm.fr</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-2544" status="OLD">
          <idno type="RNSR">199812948M</idno>
          <orgName>Laboratoire de Recherche en Informatique</orgName>
          <orgName type="acronym">LRI</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>LRI - Bâtiments 650-660 Université Paris-Sud 91405 Orsay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lri.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-92966" type="direct"/>
            <relation active="#struct-411575" type="direct"/>
            <relation name="UMR8623" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-92966" status="OLD">
          <idno type="ROR">https://ror.org/028rypz17</idno>
          <orgName>Université Paris-Sud - Paris 11</orgName>
          <orgName type="acronym">UP11</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bâtiment 300 - 91405 Orsay cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-psud.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-411575" status="VALID">
          <idno type="IdRef">184443237</idno>
          <idno type="ROR">https://ror.org/019tcpt25</idno>
          <orgName>CentraleSupélec</orgName>
          <desc>
            <address>
              <addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.centralesupelec.fr</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>