On weak odd domination and graph-based quantum secret sharing
Identifieur interne : 000320 ( Main/Exploration ); précédent : 000319; suivant : 000321On weak odd domination and graph-based quantum secret sharing
Auteurs : Sylvain Gravier [France] ; Jérôme Javelle [France] ; Mehdi Mhalla [France] ; Simon Perdrix [France]Source :
English descriptors
Abstract
A weak odd dominated (WOD) set in a graph is a subset B of vertices for which there exists a distinct set of vertices C such that every vertex in B has an odd number of neighbors in C . We point out the connections of weak odd domination with odd domination, [σ,ρ]-domination, and perfect codes. We introduce bounds on κ(G), the maximum size of WOD sets of a graph G , and on κ′(G), the minimum size of non-WOD sets of G. Moreover, we prove that the corresponding decision problems are NP-complete.The study of weak odd domination is mainly motivated by the design of graph-based quantum secret sharing protocols: a graph G of order n corresponds to a secret sharing protocol whose threshold is κQ(G)=max(κ(G),n−κ′(G)). These graph-based protocols are very promising in terms of physical implementation, however all such graph-based protocols studied in the literature have quasi-unanimity thresholds (i.e. κQ(G)=n−o(n) where n is the order of the graph G underlying the protocol). In this paper, we show using probabilistic methods the existence of graphs with smaller κQ (i.e. κQ(G)≤0.811n where n is the order of G). We also prove that deciding for a given graph G whether κQ(G)≤k is NP-complete, which means that one cannot efficiently double check that a graph randomly generated has actually a κQ smaller than 0.811n.
Url:
DOI: 10.1016/j.tcs.2015.05.038
Affiliations:
- France
- Auvergne-Rhône-Alpes, Grand Est, Lorraine (région), Rhône-Alpes
- Grenoble, Metz, Nancy
- Université Joseph Fourier, Université Pierre-Mendès-France, Université de Grenoble, Université de Lorraine
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 003884
- to stream Hal, to step Curation: 003884
- to stream Hal, to step Checkpoint: 000296
- to stream Main, to step Merge: 000320
- to stream Main, to step Curation: 000320
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">On weak odd domination and graph-based quantum secret sharing</title>
<author><name sortKey="Gravier, Sylvain" sort="Gravier, Sylvain" uniqKey="Gravier S" first="Sylvain" last="Gravier">Sylvain Gravier</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-21" status="VALID"><idno type="IdRef">033629129</idno>
<idno type="ISNI">0000000122896889</idno>
<idno type="RNSR">199512018P</idno>
<orgName>Institut Fourier</orgName>
<orgName type="acronym">IF</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www-fourier.ujf-grenoble.fr/</ref>
</desc>
<listRelation><relation active="#struct-51016" type="direct"></relation>
<relation name="UMR5582" active="#struct-441569" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-51016" type="direct"><org type="institution" xml:id="struct-51016" status="OLD"><orgName>Université Joseph Fourier</orgName>
<orgName type="acronym">UJF</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ujf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR5582" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Joseph Fourier</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
</affiliation>
</author>
<author><name sortKey="Javelle, Jerome" sort="Javelle, Jerome" uniqKey="Javelle J" first="Jérôme" last="Javelle">Jérôme Javelle</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-24471" status="VALID"><orgName>Laboratoire d'Informatique de Grenoble</orgName>
<orgName type="acronym">LIG</orgName>
<desc><address><addrLine>UMR 5217 - Laboratoire LIG - 38041 Grenoble cedex 9 - France Tél. : +33 (0)4 76 51 43 61 - Fax : +33 (0)4 76 51 49 85</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.liglab.fr/</ref>
</desc>
<listRelation><relation active="#struct-3886" type="direct"></relation>
<relation active="#struct-51016" type="direct"></relation>
<relation active="#struct-300275" type="direct"></relation>
<relation name="UMR5217" active="#struct-441569" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-3886" type="direct"><org type="institution" xml:id="struct-3886" status="OLD"><orgName>Université Pierre Mendès France</orgName>
<orgName type="acronym">Grenoble 2 UPMF</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>BP 47 - 38040 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.upmf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-51016" type="direct"><org type="institution" xml:id="struct-51016" status="OLD"><orgName>Université Joseph Fourier</orgName>
<orgName type="acronym">UJF</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ujf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300275" type="direct"><org type="institution" xml:id="struct-300275" status="VALID"><orgName>Institut National Polytechnique de Grenoble (INPG)</orgName>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle name="UMR5217" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Pierre-Mendès-France</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Joseph Fourier</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
</affiliation>
</author>
<author><name sortKey="Mhalla, Mehdi" sort="Mhalla, Mehdi" uniqKey="Mhalla M" first="Mehdi" last="Mhalla">Mehdi Mhalla</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-389148" status="INCOMING"><orgName>CAPP</orgName>
<desc><address><country key="FR"></country>
</address>
</desc>
<listRelation><relation active="#struct-24471" type="direct"></relation>
<relation active="#struct-3886" type="indirect"></relation>
<relation active="#struct-51016" type="indirect"></relation>
<relation active="#struct-300275" type="indirect"></relation>
<relation name="UMR5217" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-24471" type="direct"><org type="laboratory" xml:id="struct-24471" status="VALID"><orgName>Laboratoire d'Informatique de Grenoble</orgName>
<orgName type="acronym">LIG</orgName>
<desc><address><addrLine>UMR 5217 - Laboratoire LIG - 38041 Grenoble cedex 9 - France Tél. : +33 (0)4 76 51 43 61 - Fax : +33 (0)4 76 51 49 85</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.liglab.fr/</ref>
</desc>
<listRelation><relation active="#struct-3886" type="direct"></relation>
<relation active="#struct-51016" type="direct"></relation>
<relation active="#struct-300275" type="direct"></relation>
<relation name="UMR5217" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-3886" type="indirect"><org type="institution" xml:id="struct-3886" status="OLD"><orgName>Université Pierre Mendès France</orgName>
<orgName type="acronym">Grenoble 2 UPMF</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>BP 47 - 38040 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.upmf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-51016" type="indirect"><org type="institution" xml:id="struct-51016" status="OLD"><orgName>Université Joseph Fourier</orgName>
<orgName type="acronym">UJF</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ujf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300275" type="indirect"><org type="institution" xml:id="struct-300275" status="VALID"><orgName>Institut National Polytechnique de Grenoble (INPG)</orgName>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle name="UMR5217" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Pierre-Mendès-France</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Joseph Fourier</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
</affiliation>
</author>
<author><name sortKey="Perdrix, Simon" sort="Perdrix, Simon" uniqKey="Perdrix S" first="Simon" last="Perdrix">Simon Perdrix</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-29797" status="VALID"><idno type="RNSR">200918992J</idno>
<orgName>Theoretical adverse computations, and safety</orgName>
<orgName type="acronym">CARTE</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/carte</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423084" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><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"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423084" type="direct"><org type="department" xml:id="struct-423084" status="VALID"><orgName>Department of Formal Methods </orgName>
<orgName type="acronym">LORIA - FM</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/formal-methods</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-01249271</idno>
<idno type="halId">hal-01249271</idno>
<idno type="halUri">https://hal.inria.fr/hal-01249271</idno>
<idno type="url">https://hal.inria.fr/hal-01249271</idno>
<idno type="doi">10.1016/j.tcs.2015.05.038</idno>
<date when="2015-09-20">2015-09-20</date>
<idno type="wicri:Area/Hal/Corpus">003884</idno>
<idno type="wicri:Area/Hal/Curation">003884</idno>
<idno type="wicri:Area/Hal/Checkpoint">000296</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">000296</idno>
<idno type="wicri:Area/Main/Merge">000320</idno>
<idno type="wicri:Area/Main/Curation">000320</idno>
<idno type="wicri:Area/Main/Exploration">000320</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">On weak odd domination and graph-based quantum secret sharing</title>
<author><name sortKey="Gravier, Sylvain" sort="Gravier, Sylvain" uniqKey="Gravier S" first="Sylvain" last="Gravier">Sylvain Gravier</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-21" status="VALID"><idno type="IdRef">033629129</idno>
<idno type="ISNI">0000000122896889</idno>
<idno type="RNSR">199512018P</idno>
<orgName>Institut Fourier</orgName>
<orgName type="acronym">IF</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www-fourier.ujf-grenoble.fr/</ref>
</desc>
<listRelation><relation active="#struct-51016" type="direct"></relation>
<relation name="UMR5582" active="#struct-441569" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-51016" type="direct"><org type="institution" xml:id="struct-51016" status="OLD"><orgName>Université Joseph Fourier</orgName>
<orgName type="acronym">UJF</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ujf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR5582" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Joseph Fourier</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
</affiliation>
</author>
<author><name sortKey="Javelle, Jerome" sort="Javelle, Jerome" uniqKey="Javelle J" first="Jérôme" last="Javelle">Jérôme Javelle</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-24471" status="VALID"><orgName>Laboratoire d'Informatique de Grenoble</orgName>
<orgName type="acronym">LIG</orgName>
<desc><address><addrLine>UMR 5217 - Laboratoire LIG - 38041 Grenoble cedex 9 - France Tél. : +33 (0)4 76 51 43 61 - Fax : +33 (0)4 76 51 49 85</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.liglab.fr/</ref>
</desc>
<listRelation><relation active="#struct-3886" type="direct"></relation>
<relation active="#struct-51016" type="direct"></relation>
<relation active="#struct-300275" type="direct"></relation>
<relation name="UMR5217" active="#struct-441569" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-3886" type="direct"><org type="institution" xml:id="struct-3886" status="OLD"><orgName>Université Pierre Mendès France</orgName>
<orgName type="acronym">Grenoble 2 UPMF</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>BP 47 - 38040 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.upmf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-51016" type="direct"><org type="institution" xml:id="struct-51016" status="OLD"><orgName>Université Joseph Fourier</orgName>
<orgName type="acronym">UJF</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ujf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300275" type="direct"><org type="institution" xml:id="struct-300275" status="VALID"><orgName>Institut National Polytechnique de Grenoble (INPG)</orgName>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle name="UMR5217" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Pierre-Mendès-France</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Joseph Fourier</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
</affiliation>
</author>
<author><name sortKey="Mhalla, Mehdi" sort="Mhalla, Mehdi" uniqKey="Mhalla M" first="Mehdi" last="Mhalla">Mehdi Mhalla</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-389148" status="INCOMING"><orgName>CAPP</orgName>
<desc><address><country key="FR"></country>
</address>
</desc>
<listRelation><relation active="#struct-24471" type="direct"></relation>
<relation active="#struct-3886" type="indirect"></relation>
<relation active="#struct-51016" type="indirect"></relation>
<relation active="#struct-300275" type="indirect"></relation>
<relation name="UMR5217" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-24471" type="direct"><org type="laboratory" xml:id="struct-24471" status="VALID"><orgName>Laboratoire d'Informatique de Grenoble</orgName>
<orgName type="acronym">LIG</orgName>
<desc><address><addrLine>UMR 5217 - Laboratoire LIG - 38041 Grenoble cedex 9 - France Tél. : +33 (0)4 76 51 43 61 - Fax : +33 (0)4 76 51 49 85</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.liglab.fr/</ref>
</desc>
<listRelation><relation active="#struct-3886" type="direct"></relation>
<relation active="#struct-51016" type="direct"></relation>
<relation active="#struct-300275" type="direct"></relation>
<relation name="UMR5217" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-3886" type="indirect"><org type="institution" xml:id="struct-3886" status="OLD"><orgName>Université Pierre Mendès France</orgName>
<orgName type="acronym">Grenoble 2 UPMF</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>BP 47 - 38040 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.upmf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-51016" type="indirect"><org type="institution" xml:id="struct-51016" status="OLD"><orgName>Université Joseph Fourier</orgName>
<orgName type="acronym">UJF</orgName>
<date type="end">2015-12-31</date>
<desc><address><addrLine>BP 53 - 38041 Grenoble Cedex 9</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.ujf-grenoble.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300275" type="indirect"><org type="institution" xml:id="struct-300275" status="VALID"><orgName>Institut National Polytechnique de Grenoble (INPG)</orgName>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle name="UMR5217" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Pierre-Mendès-France</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
<placeName><settlement type="city">Grenoble</settlement>
<region type="region" nuts="2">Auvergne-Rhône-Alpes</region>
<region type="old region" nuts="2">Rhône-Alpes</region>
</placeName>
<orgName type="university">Université Joseph Fourier</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Grenoble</orgName>
</affiliation>
</author>
<author><name sortKey="Perdrix, Simon" sort="Perdrix, Simon" uniqKey="Perdrix S" first="Simon" last="Perdrix">Simon Perdrix</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-29797" status="VALID"><idno type="RNSR">200918992J</idno>
<orgName>Theoretical adverse computations, and safety</orgName>
<orgName type="acronym">CARTE</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/carte</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423084" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><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"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423084" type="direct"><org type="department" xml:id="struct-423084" status="VALID"><orgName>Department of Formal Methods </orgName>
<orgName type="acronym">LORIA - FM</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/formal-methods</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</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"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
</analytic>
<idno type="DOI">10.1016/j.tcs.2015.05.038</idno>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term> Graph theory</term>
<term> NP-completeness</term>
<term> Quantum information</term>
<term>Complexity</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">A weak odd dominated (WOD) set in a graph is a subset B of vertices for which there exists a distinct set of vertices C such that every vertex in B has an odd number of neighbors in C . We point out the connections of weak odd domination with odd domination, [σ,ρ]-domination, and perfect codes. We introduce bounds on κ(G), the maximum size of WOD sets of a graph G , and on κ′(G), the minimum size of non-WOD sets of G. Moreover, we prove that the corresponding decision problems are NP-complete.The study of weak odd domination is mainly motivated by the design of graph-based quantum secret sharing protocols: a graph G of order n corresponds to a secret sharing protocol whose threshold is κQ(G)=max(κ(G),n−κ′(G)). These graph-based protocols are very promising in terms of physical implementation, however all such graph-based protocols studied in the literature have quasi-unanimity thresholds (i.e. κQ(G)=n−o(n) where n is the order of the graph G underlying the protocol). In this paper, we show using probabilistic methods the existence of graphs with smaller κQ (i.e. κQ(G)≤0.811n where n is the order of G). We also prove that deciding for a given graph G whether κQ(G)≤k is NP-complete, which means that one cannot efficiently double check that a graph randomly generated has actually a κQ smaller than 0.811n.</div>
</front>
</TEI>
<affiliations><list><country><li>France</li>
</country>
<region><li>Auvergne-Rhône-Alpes</li>
<li>Grand Est</li>
<li>Lorraine (région)</li>
<li>Rhône-Alpes</li>
</region>
<settlement><li>Grenoble</li>
<li>Metz</li>
<li>Nancy</li>
</settlement>
<orgName><li>Université Joseph Fourier</li>
<li>Université Pierre-Mendès-France</li>
<li>Université de Grenoble</li>
<li>Université de Lorraine</li>
</orgName>
</list>
<tree><country name="France"><region name="Auvergne-Rhône-Alpes"><name sortKey="Gravier, Sylvain" sort="Gravier, Sylvain" uniqKey="Gravier S" first="Sylvain" last="Gravier">Sylvain Gravier</name>
</region>
<name sortKey="Javelle, Jerome" sort="Javelle, Jerome" uniqKey="Javelle J" first="Jérôme" last="Javelle">Jérôme Javelle</name>
<name sortKey="Mhalla, Mehdi" sort="Mhalla, Mehdi" uniqKey="Mhalla M" first="Mehdi" last="Mhalla">Mehdi Mhalla</name>
<name sortKey="Perdrix, Simon" sort="Perdrix, Simon" uniqKey="Perdrix S" first="Simon" last="Perdrix">Simon Perdrix</name>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000320 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000320 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Lorraine |area= InforLorV4 |flux= Main |étape= Exploration |type= RBID |clé= Hal:hal-01249271 |texte= On weak odd domination and graph-based quantum secret sharing }}
This area was generated with Dilib version V0.6.33. |