<?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-00429822</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="2026-04-29T20:19:45+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">The Proportional Colouring Problem: Optimizing Buffers in Radio Mesh Networks</title>
            <author role="aut">
              <persName>
                <forename type="first">Florian</forename>
                <surname>Huc</surname>
              </persName>
              <idno type="halauthorid">142658-0</idno>
              <affiliation ref="#struct-2466"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Claudia</forename>
                <surname>Linhares Sales</surname>
              </persName>
              <idno type="halauthorid">168597-0</idno>
              <orgName ref="#struct-117182"/>
              <affiliation ref="#struct-78038"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Hervé</forename>
                <surname>Rivano</surname>
              </persName>
              <email type="md5">c18470c22ca2bc4eba90ed1cbfd2548e</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">herve-rivano</idno>
              <idno type="idhal" notation="numeric">1193</idno>
              <idno type="halauthorid" notation="string">16512-1193</idno>
              <idno type="IDREF">https://www.idref.fr/078642256</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-6112-7468</idno>
              <affiliation ref="#struct-2466"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Hervé</forename>
                <surname>Rivano</surname>
              </persName>
              <email type="md5">c18470c22ca2bc4eba90ed1cbfd2548e</email>
              <email type="domain">inria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2009-11-04 15:57:14</date>
              <date type="whenModified">2025-10-07 15:32:02</date>
              <date type="whenReleased">2009-11-04 16:03:40</date>
              <date type="whenProduced">2008-02</date>
              <date type="whenEndEmbargoed">2009-11-04</date>
              <ref type="file" target="https://hal.science/hal-00429822v1/document">
                <date notBefore="2009-11-04"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00429822v1/file/HLR07.pdf" id="file-429822-236385">
                <date notBefore="2009-11-04"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="113263">
                <persName>
                  <forename>Hervé</forename>
                  <surname>Rivano</surname>
                </persName>
                <email type="md5">c18470c22ca2bc4eba90ed1cbfd2548e</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00429822</idno>
            <idno type="halUri">https://hal.science/hal-00429822</idno>
            <idno type="halBibtex">huc:hal-00429822</idno>
            <idno type="halRefHtml">&lt;i&gt;The IV Latin-American Algorithms, Graphs, and Optimization Symposium (LAGOS 07)&lt;/i&gt;, Feb 2008, Puerto Varas, Chile. pp.141--146</idno>
            <idno type="halRef">The IV Latin-American Algorithms, Graphs, and Optimization Symposium (LAGOS 07), Feb 2008, Puerto Varas, Chile. pp.141--146</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-429822-236385"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNICE">Université Nice Sophia Antipolis</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA-SOPHIA">INRIA Sophia Antipolis - Méditerranée</idno>
            <idno type="stamp" n="I3S">Laboratoire d'Informatique, Signaux et Systèmes de Sophia-Antipolis</idno>
            <idno type="stamp" n="INRIASO">INRIA-SOPHIA</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="UNIV-COTEDAZUR">Université Côte d'Azur</idno>
            <idno type="stamp" n="TEST-NICE">test nice</idno>
          </seriesStmt>
          <notesStmt>
            <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">The Proportional Colouring Problem: Optimizing Buffers in Radio Mesh Networks</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Florian</forename>
                    <surname>Huc</surname>
                  </persName>
                  <idno type="halauthorid">142658-0</idno>
                  <affiliation ref="#struct-2466"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Claudia</forename>
                    <surname>Linhares Sales</surname>
                  </persName>
                  <idno type="halauthorid">168597-0</idno>
                  <orgName ref="#struct-117182"/>
                  <affiliation ref="#struct-78038"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Hervé</forename>
                    <surname>Rivano</surname>
                  </persName>
                  <email type="md5">c18470c22ca2bc4eba90ed1cbfd2548e</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">herve-rivano</idno>
                  <idno type="idhal" notation="numeric">1193</idno>
                  <idno type="halauthorid" notation="string">16512-1193</idno>
                  <idno type="IDREF">https://www.idref.fr/078642256</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-6112-7468</idno>
                  <affiliation ref="#struct-2466"/>
                </author>
              </analytic>
              <monogr>
                <title level="m">The IV Latin-American Algorithms, Graphs, and Optimization Symposium (LAGOS 07)</title>
                <meeting>
                  <title>The IV Latin-American Algorithms, Graphs, and Optimization Symposium (LAGOS 07)</title>
                  <date type="start">2008-02</date>
                  <settlement>Puerto Varas</settlement>
                  <country key="CL">Chile</country>
                </meeting>
                <imprint>
                  <biblScope unit="serie">Electronic Notes in Discrete Mathematics</biblScope>
                  <biblScope unit="volume">30</biblScope>
                  <biblScope unit="pp">141--146</biblScope>
                  <date type="datePub">2008-02</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="info.info-ni">Computer Science [cs]/Networking and Internet Architecture [cs.NI]</classCode>
              <classCode scheme="halDomain" n="info.info-ds">Computer Science [cs]/Data Structures and Algorithms [cs.DS]</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 paper, we consider a new edge colouring problem: the proportional edge-colouring. Given a graph $G$ with positive weights associated to its edges, we want to find a colouring which preserves the proportion given by the weights associated to each edge. If such colouring exists, we want to find one using a minimum number of colours. We proved that deciding if a weighted graph admits a proportional colouring is polynomial while determining its proportional chromatic index is NP-hard. In addition, we give a lower bound and an upper bound for this parameter that can be computed in polynomial time. We finally show a class of graphs and a class of weighted graphs for which we can exactly determine the proportional chromatic index.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-2466" status="OLD">
          <idno type="RNSR">200018393X</idno>
          <orgName>Algorithms, simulation, combinatorics and optimization for telecommunications</orgName>
          <orgName type="acronym">MASCOTTE</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-34586" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-451999" type="direct"/>
            <relation active="#struct-13009" type="indirect"/>
            <relation active="#struct-117617" type="indirect"/>
            <relation name="UMR7271" active="#struct-441569" type="indirect"/>
            <relation active="#struct-1039632" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-78038" status="VALID">
          <orgName>Laboratórios de PesquIsa em ComputAção</orgName>
          <orgName type="acronym">LIA</orgName>
          <desc>
            <address>
              <addrLine>DC/UFC Campos do Pici, Bloco 910 60455-760 Fortaleza, CE Brazil</addrLine>
              <country key="BR"/>
            </address>
            <ref type="url">http://www.lia.ufc.br/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-117182" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-34586" status="VALID">
          <idno type="RNSR">198318250R</idno>
          <idno type="ROR">https://ror.org/01nzkaw91</idno>
          <orgName>Centre Inria d'Université Côte d'Azur</orgName>
          <desc>
            <address>
              <addrLine>2004 route des Lucioles BP 93 06902 Sophia Antipolis</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/sophia/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="department" xml:id="struct-451999" status="VALID">
          <orgName>COMmunications, Réseaux, systèmes Embarqués et Distribués</orgName>
          <orgName type="acronym">Laboratoire I3S - COMRED</orgName>
          <date type="start">2016-03-02</date>
          <desc>
            <address>
              <addrLine>Laboratoire I3SCS 4012106903 Sophia Antipolis Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.i3s.unice.fr/comred</ref>
          </desc>
          <listRelation>
            <relation active="#struct-13009" type="direct"/>
            <relation active="#struct-117617" type="indirect"/>
            <relation name="UMR7271" active="#struct-441569" type="indirect"/>
            <relation active="#struct-1039632" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-13009" status="VALID">
          <idno type="IdRef">050320491</idno>
          <idno type="ISNI">0000000105613840</idno>
          <idno type="RNSR">201220432L</idno>
          <idno type="ROR">https://ror.org/01215r597</idno>
          <orgName>Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis</orgName>
          <orgName type="acronym">I3S</orgName>
          <desc>
            <address>
              <addrLine>2000, route des Lucioles - Les Algorithmes - bât. Euclide B 06900 Sophia Antipolis</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.i3s.unice.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-117617" type="direct"/>
            <relation name="UMR7271" active="#struct-441569" type="direct"/>
            <relation active="#struct-1039632" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-117617" status="VALID">
          <idno type="IdRef">026403498</idno>
          <idno type="ISNI">0000000123372892</idno>
          <idno type="ROR">https://ror.org/02k9vew78</idno>
          <orgName>Université Nice Sophia Antipolis (1965 - 2019)</orgName>
          <orgName type="acronym">UNS</orgName>
          <date type="start">1965-10-23</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Parc Valrose, 06100 Nice</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://unice.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="regroupinstitution" xml:id="struct-1039632" status="VALID">
          <idno type="IdRef">241035694</idno>
          <idno type="ROR">https://ror.org/019tgvf94</idno>
          <orgName>Université Côte d'Azur</orgName>
          <orgName type="acronym">UniCA</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Parc Valrose, 28, avenue Valrose 06108 Nice Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://univ-cotedazur.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-117182" status="VALID">
          <idno type="ISNI">0000 0001 2160 0329</idno>
          <idno type="ROR">https://ror.org/03srtnf24</idno>
          <orgName>Universidade Federal do Ceará = Federal University of Ceará</orgName>
          <orgName type="acronym">UFC</orgName>
          <desc>
            <address>
              <addrLine>Av. da Universidade, 2853 - Benfica, Fortaleza - CE, CEP 60020-181</addrLine>
              <country key="BR"/>
            </address>
            <ref type="url">http://www.ufc.br/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>