<?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 inria-00073820</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="2026-05-19T04:59:45+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Optimal Line Bipartitions of Point Sets</title>
            <author role="aut">
              <persName>
                <forename type="first">Olivier</forename>
                <surname>Devillers</surname>
              </persName>
              <email type="md5">84567043a7422b2d5b62fbb616826026</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">olivierdevillers</idno>
              <idno type="idhal" notation="numeric">2232</idno>
              <idno type="halauthorid" notation="string">26407-2232</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-4275-5068</idno>
              <idno type="GOOGLE SCHOLAR">http://scholar.google.com/citations?user=oD-iXjcAAAAJ</idno>
              <idno type="IDREF">https://www.idref.fr/033684162</idno>
              <orgName ref="#struct-300009"/>
              <affiliation ref="#struct-2476"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Matthew J.</forename>
                <surname>Katz</surname>
              </persName>
              <idno type="halauthorid">144948-0</idno>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Rapport De Recherche</forename>
                <surname>Inria</surname>
              </persName>
              <email type="md5">5abb5e81fa75e038ad4538c1220f4652</email>
              <email type="domain">inria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2006-05-24 13:49:48</date>
              <date type="whenWritten">1996-04</date>
              <date type="whenModified">2025-08-26 15:21:01</date>
              <date type="whenReleased">2006-05-31 14:24:28</date>
              <date type="whenProduced">1996-04</date>
              <date type="whenEndEmbargoed">2006-05-24</date>
              <ref type="file" target="https://inria.hal.science/inria-00073820v1/document">
                <date notBefore="2006-05-24"/>
              </ref>
              <ref type="file" n="1" target="https://inria.hal.science/inria-00073820v1/file/RR-2871.pdf" id="file-73820-689973">
                <date notBefore="2006-05-24"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="111068">
                <persName>
                  <forename>Rapport De Recherche</forename>
                  <surname>Inria</surname>
                </persName>
                <email type="md5">5abb5e81fa75e038ad4538c1220f4652</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">inria-00073820</idno>
            <idno type="halUri">https://inria.hal.science/inria-00073820</idno>
            <idno type="halBibtex">devillers:inria-00073820</idno>
            <idno type="halRefHtml">RR-2871, INRIA. 1996</idno>
            <idno type="halRef">RR-2871, INRIA. 1996</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-73820-689973"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <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="INRIA-RRRT">Rapports de recherche et Technique de l'Inria</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="LARA">LARA</idno>
            <idno type="stamp" n="UNIV-COTEDAZUR">Université Côte d'Azur</idno>
            <idno type="stamp" n="INRIA-300009">Inria 300009</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Optimal Line Bipartitions of Point Sets</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Olivier</forename>
                    <surname>Devillers</surname>
                  </persName>
                  <email type="md5">84567043a7422b2d5b62fbb616826026</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">olivierdevillers</idno>
                  <idno type="idhal" notation="numeric">2232</idno>
                  <idno type="halauthorid" notation="string">26407-2232</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-4275-5068</idno>
                  <idno type="GOOGLE SCHOLAR">http://scholar.google.com/citations?user=oD-iXjcAAAAJ</idno>
                  <idno type="IDREF">https://www.idref.fr/033684162</idno>
                  <orgName ref="#struct-300009"/>
                  <affiliation ref="#struct-2476"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Matthew J.</forename>
                    <surname>Katz</surname>
                  </persName>
                  <idno type="halauthorid">144948-0</idno>
                </author>
              </analytic>
              <monogr>
                <idno type="reportNumber">RR-2871</idno>
                <imprint>
                  <date type="datePub">1996-04</date>
                </imprint>
                <authority type="institution">INRIA</authority>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">COMPUTATIONAL GEOMETRY</term>
                <term xml:lang="en">ARRANGEMENT</term>
                <term xml:lang="en">LOCALISATION</term>
              </keywords>
              <classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode>
              <classCode scheme="halTypology" n="REPORT">Reports</classCode>
              <classCode scheme="halOldTypology" n="REPORT">Reports</classCode>
              <classCode scheme="halTreeTypology" n="REPORT">Reports</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Let $S$ be a set of $n$ points in the plane. We study the following problem: Partition $S$ by a line into two subsets $S_a$ and $S_b$ such that $max{f(S_a), f(S_b)}$ is minimal, where $f$ is any monotone function defined over $2^S$. We first present a solution to the case where the points in $S$ are the vertices of some convex polygon and apply it to some common cases --- $f(S')$ is the perimeter / area / or width of the convex hull of $S' \subseteq S$ --- to obtain linear solutions (or $O(n\log n)$ solutions if the convex hull of $S$ is not given) to the corresponding problems. This solution is based on an efficient procedure for finding a minimal entry in matrices of some special type / which we believe is of independent interest. For the general case we present a linear space solution which is in some sense output sensitive. It yields solutions to the perimeter and area cases that are never slower and often faster than the best previous solutions.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-2476" status="OLD">
          <idno type="RNSR">198721510S</idno>
          <orgName>Geometry, Algorithms and Robotics</orgName>
          <orgName type="acronym">PRISME</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-34586" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </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>
      </listOrg>
    </back>
  </text>
</TEI>