<?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-01262822</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="2026-05-10T02:09:55+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">The k-separator problem : polyhedra, complexity and approximation results</title>
            <author role="aut">
              <persName>
                <forename type="first">Walid</forename>
                <surname>Ben-Ameur</surname>
              </persName>
              <email type="md5">1d946490d478520151c93afed4c8ad11</email>
              <email type="domain">telecom-sudparis.eu</email>
              <idno type="idhal" notation="string">walid-ben-ameur</idno>
              <idno type="idhal" notation="numeric">181491</idno>
              <idno type="halauthorid" notation="string">34752-181491</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-2865-1123</idno>
              <idno type="IDREF">https://www.idref.fr/052633152</idno>
              <affiliation ref="#struct-95599"/>
              <affiliation ref="#struct-638"/>
              <affiliation ref="#struct-441569"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Mohamed</forename>
                <forename type="middle">S. A.</forename>
                <surname>Mohamed</surname>
              </persName>
              <idno type="halauthorid">22760-0</idno>
              <affiliation ref="#struct-95599"/>
              <affiliation ref="#struct-638"/>
              <affiliation ref="#struct-441569"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">José</forename>
                <surname>Neto</surname>
              </persName>
              <email type="md5">4fd95420ae6c3aa855ea3a9f2086e47c</email>
              <email type="domain">telecom-sudparis.eu</email>
              <idno type="idhal" notation="string">jose-neto</idno>
              <idno type="idhal" notation="numeric">176721</idno>
              <idno type="halauthorid" notation="string">29835-176721</idno>
              <idno type="IDREF">https://www.idref.fr/082329966</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-5354-4816</idno>
              <affiliation ref="#struct-95599"/>
              <affiliation ref="#struct-638"/>
              <affiliation ref="#struct-441569"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Médiathèque</forename>
                <surname>Télécom SudParis &amp; Institut Mines-Télécom Business School</surname>
              </persName>
              <email type="md5">8d9568058c47dcee2bc21ac2481f44c9</email>
              <email type="domain">imtbs-tsp.eu</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2016-01-27 11:30:26</date>
              <date type="whenModified">2026-02-07 05:12:14</date>
              <date type="whenReleased">2016-01-27 11:30:26</date>
              <date type="whenProduced">2015-01</date>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="142673">
                <persName>
                  <forename>Médiathèque</forename>
                  <surname>Télécom SudParis &amp; Institut Mines-Télécom Business School</surname>
                </persName>
                <email type="md5">8d9568058c47dcee2bc21ac2481f44c9</email>
                <email type="domain">imtbs-tsp.eu</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01262822</idno>
            <idno type="halUri">https://hal.science/hal-01262822</idno>
            <idno type="halBibtex">benameur:hal-01262822</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Combinatorial Optimization&lt;/i&gt;, 2015, 29 (1), pp.276 - 307. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s10878-014-9753-x"&gt;&amp;#x27E8;10.1007/s10878-014-9753-x&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of Combinatorial Optimization, 2015, 29 (1), pp.276 - 307. &amp;#x27E8;10.1007/s10878-014-9753-x&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="TELECOM-SUDPARIS" corresp="INSTITUT-MINES-TELECOM">Télécom SudParis</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="INSTITUTS-TELECOM">composantes instituts telecom </idno>
            <idno type="stamp" n="INSTITUT-MINES-TELECOM">Institut Mines Telecom</idno>
            <idno type="stamp" n="IP-PARIS-DEPARTEMENT-MATHEMATIQUES">Département de Mathèmatiques</idno>
            <idno type="stamp" n="IP-PARIS-MATHEMATIQUES">IP Paris Département de Mathématiques</idno>
            <idno type="stamp" n="SAMOVAR">Services répartis, Architectures, Modélisation, Validation, Administration des Réseaux</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">The k-separator problem : polyhedra, complexity and approximation results</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Walid</forename>
                    <surname>Ben-Ameur</surname>
                  </persName>
                  <email type="md5">1d946490d478520151c93afed4c8ad11</email>
                  <email type="domain">telecom-sudparis.eu</email>
                  <idno type="idhal" notation="string">walid-ben-ameur</idno>
                  <idno type="idhal" notation="numeric">181491</idno>
                  <idno type="halauthorid" notation="string">34752-181491</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-2865-1123</idno>
                  <idno type="IDREF">https://www.idref.fr/052633152</idno>
                  <affiliation ref="#struct-95599"/>
                  <affiliation ref="#struct-638"/>
                  <affiliation ref="#struct-441569"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Mohamed</forename>
                    <forename type="middle">S. A.</forename>
                    <surname>Mohamed</surname>
                  </persName>
                  <idno type="halauthorid">22760-0</idno>
                  <affiliation ref="#struct-95599"/>
                  <affiliation ref="#struct-638"/>
                  <affiliation ref="#struct-441569"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">José</forename>
                    <surname>Neto</surname>
                  </persName>
                  <email type="md5">4fd95420ae6c3aa855ea3a9f2086e47c</email>
                  <email type="domain">telecom-sudparis.eu</email>
                  <idno type="idhal" notation="string">jose-neto</idno>
                  <idno type="idhal" notation="numeric">176721</idno>
                  <idno type="halauthorid" notation="string">29835-176721</idno>
                  <idno type="IDREF">https://www.idref.fr/082329966</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-5354-4816</idno>
                  <affiliation ref="#struct-95599"/>
                  <affiliation ref="#struct-638"/>
                  <affiliation ref="#struct-441569"/>
                </author>
              </analytic>
              <monogr>
                <idno type="localRef">14903</idno>
                <idno type="halJournalId" status="VALID">15251</idno>
                <idno type="issn">1382-6905</idno>
                <idno type="eissn">1573-2886</idno>
                <title level="j">Journal of Combinatorial Optimization</title>
                <imprint>
                  <publisher>Springer Verlag</publisher>
                  <biblScope unit="volume">29</biblScope>
                  <biblScope unit="issue">1</biblScope>
                  <biblScope unit="pp">276 - 307</biblScope>
                  <date type="datePub">2015-01</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1007/s10878-014-9753-x</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Polyhedra</term>
                <term xml:lang="en">Approximation algorithms</term>
                <term xml:lang="en">Optimization</term>
                <term xml:lang="en">Complexity theory</term>
                <term xml:lang="en">Graph partitioning</term>
              </keywords>
              <classCode scheme="halDomain" n="info.info-dm">Computer Science [cs]/Discrete Mathematics [cs.DM]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Given a vertex-weighted undirected graph G=(V,E,w) and a positive integer k, we consider the k-separator problem: it consists in finding a minimum-weight subset of vertices whose removal leads to a graph where the size of each connected component is less than or equal to k. We show that this problem can be solved in polynomial time for some graph classes including bounded treewidth, mK2-free, (G1,G2,G3,P6)-free, interval-filament, asteroidal triple-free, weakly chordal, interval and circular-arc graphs. Polyhedral results with respect to the convex hull of the incidence vectors of k-separators are reported. Approximation algorithms are also presented </p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="department" xml:id="struct-95599" status="VALID">
          <orgName>Département Réseaux et Services Multimédia Mobiles</orgName>
          <orgName type="acronym">TSP - RS2M</orgName>
          <desc>
            <address>
              <addrLine>Télécom SudParis - 9 rue Charles Fourier - 91011 Évry cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://rs2m.telecom-sudparis.eu/fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-352124" type="direct"/>
            <relation active="#struct-302102" type="indirect"/>
            <relation name="563936" active="#struct-563936" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-638" status="VALID">
          <idno type="IdRef">281286515</idno>
          <idno type="ISNI">0000000403830480</idno>
          <idno type="RNSR">200319330C</idno>
          <orgName>Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux</orgName>
          <orgName type="acronym">SAMOVAR</orgName>
          <desc>
            <address>
              <addrLine>Télécom Sudparis, 9 rue Charles Fourier -91011 Evry cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://samovar.telecom-sudparis.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-352124" type="direct"/>
            <relation active="#struct-302102" type="indirect"/>
            <relation name="563936" active="#struct-563936" type="indirect"/>
          </listRelation>
        </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="institution" xml:id="struct-352124" status="VALID">
          <idno type="IdRef">162347510</idno>
          <idno type="ISNI">0000000406406351</idno>
          <idno type="ROR">https://ror.org/05xvk4r52</idno>
          <idno type="Wikidata">Q43305</idno>
          <orgName>Télécom SudParis</orgName>
          <orgName type="acronym">TSP</orgName>
          <desc>
            <address>
              <addrLine>9 rue Charles Fourier -91011 Evry Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.telecom-sudparis.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-302102" type="direct"/>
            <relation name="563936" active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-302102" status="VALID">
          <idno type="IdRef">192427156</idno>
          <idno type="ISNI">000000012202567X</idno>
          <idno type="ROR">https://ror.org/025vp2923</idno>
          <idno type="Wikidata">Q27962533</idno>
          <orgName>Institut Mines-Télécom [Paris]</orgName>
          <orgName type="acronym">IMT</orgName>
          <date type="start">2012-03-01</date>
          <desc>
            <address>
              <addrLine>19 Place Marguerite Perey, 91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.imt.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>