<?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-01710032</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="2026-05-03T03:58:55+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">The S-labeling problem: An algorithmic tour</title>
            <author role="aut">
              <persName>
                <forename type="first">Guillaume</forename>
                <surname>Fertin</surname>
              </persName>
              <email type="md5">e617d377105f08911523aec7e7a39202</email>
              <email type="domain">univ-nantes.fr</email>
              <idno type="idhal" notation="string">guillaume-fertin</idno>
              <idno type="idhal" notation="numeric">11485</idno>
              <idno type="halauthorid" notation="string">1943-11485</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-8251-2012</idno>
              <idno type="IDREF">https://www.idref.fr/095050612</idno>
              <affiliation ref="#struct-473973"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Irena</forename>
                <surname>Rusu</surname>
              </persName>
              <email type="md5">fad06b2c8c38ed2abdc2c970d8d5a5df</email>
              <email type="domain">univ-nantes.fr</email>
              <idno type="idhal" notation="string">irena</idno>
              <idno type="idhal" notation="numeric">16772</idno>
              <idno type="halauthorid" notation="string">1942-16772</idno>
              <idno type="IDREF">https://www.idref.fr/095050671</idno>
              <affiliation ref="#struct-473973"/>
            </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-3210"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Stéphane</forename>
                <surname>Vialette</surname>
              </persName>
              <email type="md5">57f9bd64dbe2de8e92c394b5e7463974</email>
              <email type="domain">univ-eiffel.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2018-02-15 15:16:50</date>
              <date type="whenModified">2026-04-02 11:58:01</date>
              <date type="whenReleased">2018-02-15 15:16:50</date>
              <date type="whenProduced">2018</date>
              <ref type="externalLink" target="https://doi.org/10.1016/j.dam.2017.07.036"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="135213">
                <persName>
                  <forename>Stéphane</forename>
                  <surname>Vialette</surname>
                </persName>
                <email type="md5">57f9bd64dbe2de8e92c394b5e7463974</email>
                <email type="domain">univ-eiffel.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01710032</idno>
            <idno type="halUri">https://hal.science/hal-01710032</idno>
            <idno type="halBibtex">fertin:hal-01710032</idno>
            <idno type="halRefHtml">&lt;i&gt;Discrete Applied Mathematics&lt;/i&gt;, 2018, 246, pp.49-61. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.dam.2017.07.036"&gt;&amp;#x27E8;10.1016/j.dam.2017.07.036&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Discrete Applied Mathematics, 2018, 246, pp.49-61. &amp;#x27E8;10.1016/j.dam.2017.07.036&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-NANTES">Université de Nantes</idno>
            <idno type="stamp" n="ENPC" corresp="PARISTECH">École nationale des ponts et chaussées </idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="EC-NANTES">Ecole Centrale de Nantes</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</idno>
            <idno type="stamp" n="ENPC-LIGM" corresp="ENPC">Laboratoire d'informatique Gaspard-Monge</idno>
            <idno type="stamp" n="LIGM" corresp="ENPC">Laboratoire d'informatique Gaspard-Monge</idno>
            <idno type="stamp" n="CV_LIGM" corresp="CV_UNIV-MLV">CV des membres du LIGM</idno>
            <idno type="stamp" n="UNAM">l'unam - université nantes angers le mans</idno>
            <idno type="stamp" n="LIGM_MOA" corresp="LIGM">Models and Algorithms</idno>
            <idno type="stamp" n="LS2N">Laboratoire des Sciences du Numérique de Nantes</idno>
            <idno type="stamp" n="LS2N-COMBI" corresp="LS2N">LS2N - équipe COMBI ( Combinatoire et Bio-informatique )</idno>
            <idno type="stamp" n="ESIEE-PARIS">ESIEE Paris</idno>
            <idno type="stamp" n="INSTITUTS-TELECOM">composantes instituts telecom </idno>
            <idno type="stamp" n="UNIV-EIFFEL">Université Gustave Eiffel</idno>
            <idno type="stamp" n="UPEM-UNIVEIFFEL">Université Paris-Est Marne-la-Vallée</idno>
            <idno type="stamp" n="ESIEE-UNIVEIFFEL">ESIEE Paris</idno>
            <idno type="stamp" n="NANTES-UNIVERSITE">Nantes Université</idno>
            <idno type="stamp" n="UNIV-NANTES-AV2022">Université de Nantes</idno>
            <idno type="stamp" n="NU-CENTRALE">École Centrale de Nantes</idno>
            <idno type="stamp" n="TEST3-HALCNRS">TEST3-HALCNRS</idno>
            <idno type="stamp" n="LIGM_ADA" corresp="LIGM">Algorithmique Discrète et Applications</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 S-labeling problem: An algorithmic tour</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Guillaume</forename>
                    <surname>Fertin</surname>
                  </persName>
                  <email type="md5">e617d377105f08911523aec7e7a39202</email>
                  <email type="domain">univ-nantes.fr</email>
                  <idno type="idhal" notation="string">guillaume-fertin</idno>
                  <idno type="idhal" notation="numeric">11485</idno>
                  <idno type="halauthorid" notation="string">1943-11485</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-8251-2012</idno>
                  <idno type="IDREF">https://www.idref.fr/095050612</idno>
                  <affiliation ref="#struct-473973"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Irena</forename>
                    <surname>Rusu</surname>
                  </persName>
                  <email type="md5">fad06b2c8c38ed2abdc2c970d8d5a5df</email>
                  <email type="domain">univ-nantes.fr</email>
                  <idno type="idhal" notation="string">irena</idno>
                  <idno type="idhal" notation="numeric">16772</idno>
                  <idno type="halauthorid" notation="string">1942-16772</idno>
                  <idno type="IDREF">https://www.idref.fr/095050671</idno>
                  <affiliation ref="#struct-473973"/>
                </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-3210"/>
                </author>
              </analytic>
              <monogr>
                <idno type="localRef">ACL+</idno>
                <idno type="halJournalId" status="VALID">12621</idno>
                <idno type="issn">0166-218X</idno>
                <title level="j">Discrete Applied Mathematics</title>
                <imprint>
                  <publisher>Elsevier</publisher>
                  <biblScope unit="volume">246</biblScope>
                  <biblScope unit="pp">49-61</biblScope>
                  <date type="datePub">2018</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1016/j.dam.2017.07.036</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Algorithm</term>
                <term xml:lang="en">Graph labeling</term>
              </keywords>
              <classCode scheme="halDomain" n="info.info-ds">Computer Science [cs]/Data Structures and Algorithms [cs.DS]</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 graph G=(V,E) of order n and maximum degree Delta, the NP-complete S-labeling problem consists in finding a labeling of G, i.e. a bijective mapping phi : V -&gt; {1, 2... n}, such that SL_phi(G)=Sum_{uv \in E} min{phi(u),phi(v)} is minimized. In this paper, we study the S-labeling problem, with a particular focus on algorithmic issues. We first give intrinsic properties of optimal labelings, which will prove useful for our algorithmic study. We then provide lower bounds on SL_phi(G), together with a generic greedy algorithm, which collectively allow us to approximate the problem in several classes of graphs — in particular, we obtain constant approximation ratios for regular graphs and bounded degree graphs. We also show that deciding whether there exists a labeling phi of G such that SL_phi(G) \leq |E|+k is solvable in O*(2^(2 sqrt(k)) (2 sqrt(k))!) time, thus fixed-parameterized tractable in k. We finally show that the S-Labeling problem is polynomial-time solvable for two classes of graphs, namely split graphs and (sets of) caterpillars.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-473973" status="OLD">
          <idno type="IdRef">203637585</idno>
          <idno type="RNSR">201722241F</idno>
          <idno type="ROR">https://ror.org/02snf8m58</idno>
          <orgName>Laboratoire des Sciences du Numérique de Nantes</orgName>
          <orgName type="acronym">LS2N</orgName>
          <date type="start">2017-01-01</date>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>Université de Nantes – faculté des Sciences et Techniques (FST)2 Chemin de la HoussinièreBP 92208, 44322 Nantes Cedex 3</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ls2n.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-97058" type="direct"/>
            <relation active="#struct-93263" type="indirect"/>
            <relation active="#struct-111023" type="direct"/>
            <relation name="UMR6004" active="#struct-441569" type="direct"/>
            <relation active="#struct-481355" type="direct"/>
            <relation active="#struct-302102" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-3210" status="OLD">
          <idno type="IdRef">142877891</idno>
          <idno type="ISNI">0000000091039111</idno>
          <idno type="RNSR">200212717U</idno>
          <idno type="ROR">https://ror.org/04t50yk91</idno>
          <orgName>Laboratoire d'Informatique Gaspard-Monge</orgName>
          <orgName type="acronym">LIGM</orgName>
          <date type="start">1992-01-01</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Université de Paris-Est Marne-la-Vallée, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://ligm.u-pem.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301243" type="direct"/>
            <relation active="#struct-301545" type="direct"/>
            <relation active="#struct-302035" type="direct"/>
            <relation active="#struct-302085" type="direct"/>
            <relation name="FRA3522 / FR3522" active="#struct-441569" type="direct"/>
            <relation name="UMR8049" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-97058" status="OLD">
          <orgName>Université de Nantes - UFR des Sciences et des Techniques</orgName>
          <orgName type="acronym">UN UFR ST</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>2, rue de la Houssinière - BP 92208 - 44322 Nantes cedex 3</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sciences-techniques.univ-nantes.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-93263" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-93263" status="OLD">
          <idno type="IdRef">026403447</idno>
          <idno type="ROR">https://ror.org/03gnr7b55</idno>
          <orgName>Université de Nantes</orgName>
          <orgName type="acronym">UN</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>1, quai de Tourville - BP 13522 - 44035 Nantes cedex 1</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-nantes.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-111023" status="OLD">
          <idno type="IdRef">03063525X</idno>
          <idno type="ISNI">0000000122039289</idno>
          <idno type="ROR">https://ror.org/03nh7d505</idno>
          <orgName>École Centrale de Nantes</orgName>
          <orgName type="acronym">ECN</orgName>
          <date type="end">2021-12-31</date>
          <desc>
            <address>
              <addrLine>1 rue de la Noë - BP 92101 - 44321 Nantes cedex 3</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ec-nantes.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="institution" xml:id="struct-481355" status="VALID">
          <idno type="IdRef">202743233</idno>
          <idno type="ROR">https://ror.org/030hj3061</idno>
          <orgName>IMT Atlantique</orgName>
          <orgName type="acronym">IMT Atlantique</orgName>
          <date type="start">2017-01-01</date>
          <desc>
            <address>
              <addrLine>Campus Brest : Technopôle Brest-Iroise CS 8381829238 BREST Cedex 3 -Campus Nantes : 4, rue Alfred Kastler- La chantrerie 44300 NANTES -Campus Rennes :  2 Rue de la Châtaigneraie, 35510 CESSON SEVIGNE</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.imt-atlantique.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-302102" 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="institution" xml:id="struct-301243" status="OLD">
          <idno type="IdRef">030820499</idno>
          <idno type="ISNI">0000000115124813</idno>
          <idno type="ROR">https://ror.org/02aqt9c37</idno>
          <orgName>Université Paris-Est Marne-la-Vallée</orgName>
          <orgName type="acronym">UPEM</orgName>
          <date type="start">1991-07-22</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>5 boulevard Descartes - Champs-sur-Marne - 77454 Marne-la-Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-pem.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-301545" status="OLD">
          <idno type="ROR">https://ror.org/02nwvxz07</idno>
          <orgName>École nationale des ponts et chaussées</orgName>
          <orgName type="acronym">ENPC</orgName>
          <date type="start">1747-02-14</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>École nationale des ponts et chaussées, 6-8 avenue Blaise-Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://ecoledesponts.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-302035" status="VALID">
          <idno type="RNSR">199814079S</idno>
          <orgName>ESIEE Paris</orgName>
          <date type="start">2016-11-25</date>
          <desc>
            <address>
              <addrLine>2 boulevard Blaise PascalCité DescartesBP 9993162 Noisy-le-Grand Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.esiee.fr</ref>
          </desc>
        </org>
        <org type="regrouplaboratory" xml:id="struct-302085" status="VALID">
          <idno type="RNSR">201220485U</idno>
          <orgName>Fédération de Recherche Bézout</orgName>
          <orgName type="acronym">BEZOUT</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>5, bd Descartes, Champs-sur-Marne77455 Marne-la-Vallée Cedex 2 – France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://labex-bezout.fr/bezout-federation/</ref>
          </desc>
          <listRelation>
            <relation name="FRA3522 / FR3522" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>