Serveur d'exploration sur la recherche en informatique en Lorraine

Attention, ce site est en cours de développement !
Attention, site généré par des moyens informatiques à partir de corpus bruts.
Les informations ne sont donc pas validées.

On the Complexity of Sets of Free Lines and Line Segments Among Balls in Three Dimensions

Identifieur interne : 002C96 ( Istex/Curation ); précédent : 002C95; suivant : 002C97

On the Complexity of Sets of Free Lines and Line Segments Among Balls in Three Dimensions

Auteurs : Marc Glisse [France] ; Sylvain Lazard [France]

Source :

RBID : ISTEX:BE8A989299DDE2E0991313C4F53AF8DC7A89C78C

English descriptors

Abstract

Abstract: We present two new fundamental lower bounds on the worst-case combinatorial complexity of sets of free lines and sets of maximal free line segments in the presence of balls in three dimensions. We first prove that the set of maximal non-occluded line segments among n disjoint unit balls has complexity Ω(n 4), which matches the trivial O(n 4) upper bound. This improves the trivial Ω(n 2) bound and also the Ω(n 3) lower bound for the restricted setting of arbitrary-size balls (Devillers and Ramos, personal communication, 2001). This result settles, negatively, the natural conjecture that this set of line segments, or, equivalently, the visibility complex, has smaller worst-case complexity for disjoint fat objects than for skinny triangles. We also prove an Ω(n 3) lower bound on the complexity of the set of non-occluded lines among n balls of arbitrary radii, improving on the trivial Ω(n 2) bound. This new bound almost matches the recent O(n 3+ε ) upper bound (Rubin, 26th Annual ACM Symposium on Computational Geometry—SCG’10, pp. 58–67, 2010).

Url:
DOI: 10.1007/s00454-012-9414-8

Links toward previous steps (curation, corpus...)


Links to Exploration step

ISTEX:BE8A989299DDE2E0991313C4F53AF8DC7A89C78C

Le document en format XML

<record>
<TEI wicri:istexFullTextTei="biblStruct">
<teiHeader>
<fileDesc>
<titleStmt>
<title xml:lang="en">On the Complexity of Sets of Free Lines and Line Segments Among Balls in Three Dimensions</title>
<author>
<name sortKey="Glisse, Marc" sort="Glisse, Marc" uniqKey="Glisse M" first="Marc" last="Glisse">Marc Glisse</name>
<affiliation wicri:level="1">
<mods:affiliation>INRIA Saclay Île de France, Orsay, France</mods:affiliation>
<country xml:lang="fr">France</country>
<wicri:regionArea>INRIA Saclay Île de France, Orsay</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1">
<mods:affiliation>E-mail: marc.glisse@inria.fr</mods:affiliation>
<country wicri:rule="url">France</country>
</affiliation>
</author>
<author>
<name sortKey="Lazard, Sylvain" sort="Lazard, Sylvain" uniqKey="Lazard S" first="Sylvain" last="Lazard">Sylvain Lazard</name>
<affiliation wicri:level="1">
<mods:affiliation>LORIA laboratory, INRIA Nancy Grand Est, Nancy, France</mods:affiliation>
<country xml:lang="fr">France</country>
<wicri:regionArea>LORIA laboratory, INRIA Nancy Grand Est, Nancy</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1">
<mods:affiliation>E-mail: sylvain.lazard@inria.fr</mods:affiliation>
<country wicri:rule="url">France</country>
</affiliation>
</author>
</titleStmt>
<publicationStmt>
<idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:BE8A989299DDE2E0991313C4F53AF8DC7A89C78C</idno>
<date when="2012" year="2012">2012</date>
<idno type="doi">10.1007/s00454-012-9414-8</idno>
<idno type="url">https://api.istex.fr/ark:/67375/VQC-6LPC8G2B-7/fulltext.pdf</idno>
<idno type="wicri:Area/Istex/Corpus">002D33</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002D33</idno>
<idno type="wicri:Area/Istex/Curation">002C96</idno>
</publicationStmt>
<sourceDesc>
<biblStruct>
<analytic>
<title level="a" type="main" xml:lang="en">On the Complexity of Sets of Free Lines and Line Segments Among Balls in Three Dimensions</title>
<author>
<name sortKey="Glisse, Marc" sort="Glisse, Marc" uniqKey="Glisse M" first="Marc" last="Glisse">Marc Glisse</name>
<affiliation wicri:level="1">
<mods:affiliation>INRIA Saclay Île de France, Orsay, France</mods:affiliation>
<country xml:lang="fr">France</country>
<wicri:regionArea>INRIA Saclay Île de France, Orsay</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1">
<mods:affiliation>E-mail: marc.glisse@inria.fr</mods:affiliation>
<country wicri:rule="url">France</country>
</affiliation>
</author>
<author>
<name sortKey="Lazard, Sylvain" sort="Lazard, Sylvain" uniqKey="Lazard S" first="Sylvain" last="Lazard">Sylvain Lazard</name>
<affiliation wicri:level="1">
<mods:affiliation>LORIA laboratory, INRIA Nancy Grand Est, Nancy, France</mods:affiliation>
<country xml:lang="fr">France</country>
<wicri:regionArea>LORIA laboratory, INRIA Nancy Grand Est, Nancy</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1">
<mods:affiliation>E-mail: sylvain.lazard@inria.fr</mods:affiliation>
<country wicri:rule="url">France</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series>
<title level="j">Discrete & Computational Geometry</title>
<title level="j" type="abbrev">Discrete Comput Geom</title>
<idno type="ISSN">0179-5376</idno>
<idno type="eISSN">1432-0444</idno>
<imprint>
<publisher>Springer-Verlag</publisher>
<pubPlace>New York</pubPlace>
<date type="published" when="2012-06-01">2012-06-01</date>
<biblScope unit="volume">47</biblScope>
<biblScope unit="issue">4</biblScope>
<biblScope unit="page" from="756">756</biblScope>
<biblScope unit="page" to="772">772</biblScope>
</imprint>
<idno type="ISSN">0179-5376</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt>
<idno type="ISSN">0179-5376</idno>
</seriesStmt>
</fileDesc>
<profileDesc>
<textClass>
<keywords scheme="KwdEn" xml:lang="en">
<term>3D visibility</term>
<term>Balls</term>
<term>Free lines</term>
<term>Free segments</term>
<term>Visibility complex</term>
</keywords>
</textClass>
<langUsage>
<language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front>
<div type="abstract" xml:lang="en">Abstract: We present two new fundamental lower bounds on the worst-case combinatorial complexity of sets of free lines and sets of maximal free line segments in the presence of balls in three dimensions. We first prove that the set of maximal non-occluded line segments among n disjoint unit balls has complexity Ω(n 4), which matches the trivial O(n 4) upper bound. This improves the trivial Ω(n 2) bound and also the Ω(n 3) lower bound for the restricted setting of arbitrary-size balls (Devillers and Ramos, personal communication, 2001). This result settles, negatively, the natural conjecture that this set of line segments, or, equivalently, the visibility complex, has smaller worst-case complexity for disjoint fat objects than for skinny triangles. We also prove an Ω(n 3) lower bound on the complexity of the set of non-occluded lines among n balls of arbitrary radii, improving on the trivial Ω(n 2) bound. This new bound almost matches the recent O(n 3+ε ) upper bound (Rubin, 26th Annual ACM Symposium on Computational Geometry—SCG’10, pp. 58–67, 2010).</div>
</front>
</TEI>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Istex/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 002C96 | SxmlIndent | more

Ou

HfdSelect -h $EXPLOR_AREA/Data/Istex/Curation/biblio.hfd -nk 002C96 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Lorraine
   |area=    InforLorV4
   |flux=    Istex
   |étape=   Curation
   |type=    RBID
   |clé=     ISTEX:BE8A989299DDE2E0991313C4F53AF8DC7A89C78C
   |texte=   On the Complexity of Sets of Free Lines and Line Segments Among Balls in Three Dimensions
}}

Wicri

This area was generated with Dilib version V0.6.33.
Data generation: Mon Jun 10 21:56:28 2019. Site generation: Fri Feb 25 15:29:27 2022