Operator Calculus Algorithms for Multi-Constrained Paths
Identifieur interne : 000794 ( Main/Exploration ); précédent : 000793; suivant : 000795Operator Calculus Algorithms for Multi-Constrained Paths
Auteurs : Jamila Ben Slimane [Tunisie] ; Schott René [France] ; Yeqiong Song [France] ; G. Stacey Staples [États-Unis] ; Evangelia Tsiontsiou [France] ; Ye-Qiong Song [France]Source :
English descriptors
Abstract
Classical approaches to multi-constrained routing problems gener-ally require construction of trees and the use of heuristics to preventcombinatorial explosion. Introduced here is the notion of constrainedpath algebras and their application to multi-constrained path prob-lems. The inherent combinatorial properties of these algebras makethem useful for routing problems by implicitly pruning the underlyingtree structures. Operator calculus (OC) methods are generalized tomultiple non-additive constraints in order to develop algorithms forthe multi constrained path problem and multi constrained optimiza-tion problem. Theoretical underpinnings are developed first, thenalgorithms are presented. These algorithms demonstrate the tremen-dous simplicity, flexibility and speed of the OC approach. Algorithmsare implemented inMathematicaandJavaand applied to a problemfirst proposed by Ben Slimaneet al.as an example.
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Stacey Staples</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-25888" status="VALID"><orgName>Department of Mathematics and Statistics - Southern Illinois University</orgName><desc><address><addrLine>College of Arts and Sciences ; Southern Illinois University Edwardsville ; Edwardsville, Illinois 62026</addrLine><country key="US"></country></address><ref type="url">http://www.siue.edu/artsandsciences/math/</ref></desc><listRelation><relation active="#struct-300932" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300932" type="direct"><org type="institution" xml:id="struct-300932" status="VALID"><orgName>Southern Illinois University Edwardsville</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle></tutelles></hal:affiliation><country>États-Unis</country></affiliation></author><author><name sortKey="Tsiontsiou, Evangelia" sort="Tsiontsiou, Evangelia" uniqKey="Tsiontsiou E" first="Evangelia" last="Tsiontsiou">Evangelia Tsiontsiou</name><affiliation wicri:level="1"><hal:affiliation 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><tutelles><tutelle active="#struct-300009" type="direct"><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 - 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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-423085" type="direct"><org type="department" xml:id="struct-423085" status="VALID"><orgName>Department of Networks, Systems and Services</orgName><orgName type="acronym">LORIA - NSS</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.loria.fr/la-recherche-en/departements/networks-systems-and-services</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></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term> nilpotent adjacency matrix</term><term> quality of service</term><term> shortest path</term><term> zeons</term><term>Routing problems</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Classical approaches to multi-constrained routing problems gener-ally require construction of trees and the use of heuristics to preventcombinatorial explosion. Introduced here is the notion of constrainedpath algebras and their application to multi-constrained path prob-lems. The inherent combinatorial properties of these algebras makethem useful for routing problems by implicitly pruning the underlyingtree structures. Operator calculus (OC) methods are generalized tomultiple non-additive constraints in order to develop algorithms forthe multi constrained path problem and multi constrained optimiza-tion problem. Theoretical underpinnings are developed first, thenalgorithms are presented. These algorithms demonstrate the tremen-dous simplicity, flexibility and speed of the OC approach. Algorithmsare implemented inMathematicaandJavaand applied to a problemfirst proposed by Ben Slimaneet al.as an example.</div></front></TEI><affiliations><list><country><li>France</li><li>Tunisie</li><li>États-Unis</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Metz</li><li>Nancy</li></settlement><orgName><li>Université de Lorraine</li></orgName></list><tree><country name="Tunisie"><noRegion><name sortKey="Ben Slimane, Jamila" sort="Ben Slimane, Jamila" uniqKey="Ben Slimane J" first="Jamila" last="Ben Slimane">Jamila Ben Slimane</name></noRegion></country><country name="France"><region name="Grand Est"><name sortKey="Rene, Schott" sort="Rene, Schott" uniqKey="Rene S" first="Schott" last="René">Schott René</name></region><name sortKey="Song, Ye Qiong" sort="Song, Ye Qiong" uniqKey="Song Y" first="Ye-Qiong" last="Song">Ye-Qiong Song</name><name sortKey="Song, Yeqiong" sort="Song, Yeqiong" uniqKey="Song Y" first="Yeqiong" last="Song">Yeqiong Song</name><name sortKey="Tsiontsiou, Evangelia" sort="Tsiontsiou, Evangelia" uniqKey="Tsiontsiou E" first="Evangelia" last="Tsiontsiou">Evangelia Tsiontsiou</name></country><country name="États-Unis"><noRegion><name sortKey="Staples, G Stacey" sort="Staples, G Stacey" uniqKey="Staples G" first="G. Stacey" last="Staples">G. Stacey Staples</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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