Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems

Abstract Classical approaches to routing problems often employ construction of trees and the use of heuristics to prevent combinatorial explosion. The algebraic approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeo...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Schott, René [verfasserIn] Staples, G. Stacey

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	Shortest paths Message routing Semigroup algebras

Anmerkung:	© Springer Basel 2015

Übergeordnetes Werk:	Enthalten in: Advances in applied Clifford algebras - Cham (ZG) : Springer International Publishing AG, 1997, 27(2015), 1 vom: 30. Aug., Seite 45-57
Übergeordnetes Werk:	volume:27 ; year:2015 ; number:1 ; day:30 ; month:08 ; pages:45-57

Links:	Volltext

DOI / URN:	10.1007/s00006-015-0595-0

Katalog-ID:	SPR000088846

Internformat


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520			\|a Abstract Classical approaches to routing problems often employ construction of trees and the use of heuristics to prevent combinatorial explosion. The algebraic approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeon algebras. Their inherent combinatorial properties make them useful for routing problems by implicitly pruning the underlying tree structures. Through the use of generalized idempotent algebras, max-min operators can be implemented for non-additive weights. Moreover, these algebras occur as subalgebras of Clifford algebras, lending them a natural connection to quantum probability and (by extension) to quantum computing.
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700	1		\|a Staples, G. Stacey \|4 aut
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publishDate	2015
allfields	10.1007/s00006-015-0595-0 doi (DE-627)SPR000088846 (SPR)s00006-015-0595-0-e DE-627 ger DE-627 rakwb eng Schott, René verfasserin aut Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Classical approaches to routing problems often employ construction of trees and the use of heuristics to prevent combinatorial explosion. The algebraic approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeon algebras. Their inherent combinatorial properties make them useful for routing problems by implicitly pruning the underlying tree structures. Through the use of generalized idempotent algebras, max-min operators can be implemented for non-additive weights. Moreover, these algebras occur as subalgebras of Clifford algebras, lending them a natural connection to quantum probability and (by extension) to quantum computing. Shortest paths (dpeaa)DE-He213 Message routing (dpeaa)DE-He213 Semigroup algebras (dpeaa)DE-He213 Staples, G. Stacey aut Enthalten in Advances in applied Clifford algebras Cham (ZG) : Springer International Publishing AG, 1997 27(2015), 1 vom: 30. Aug., Seite 45-57 (DE-627)507183274 (DE-600)2220151-8 1661-4909 nnns volume:27 year:2015 number:1 day:30 month:08 pages:45-57 https://dx.doi.org/10.1007/s00006-015-0595-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2015 1 30 08 45-57
spelling	10.1007/s00006-015-0595-0 doi (DE-627)SPR000088846 (SPR)s00006-015-0595-0-e DE-627 ger DE-627 rakwb eng Schott, René verfasserin aut Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Classical approaches to routing problems often employ construction of trees and the use of heuristics to prevent combinatorial explosion. The algebraic approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeon algebras. Their inherent combinatorial properties make them useful for routing problems by implicitly pruning the underlying tree structures. Through the use of generalized idempotent algebras, max-min operators can be implemented for non-additive weights. Moreover, these algebras occur as subalgebras of Clifford algebras, lending them a natural connection to quantum probability and (by extension) to quantum computing. Shortest paths (dpeaa)DE-He213 Message routing (dpeaa)DE-He213 Semigroup algebras (dpeaa)DE-He213 Staples, G. Stacey aut Enthalten in Advances in applied Clifford algebras Cham (ZG) : Springer International Publishing AG, 1997 27(2015), 1 vom: 30. Aug., Seite 45-57 (DE-627)507183274 (DE-600)2220151-8 1661-4909 nnns volume:27 year:2015 number:1 day:30 month:08 pages:45-57 https://dx.doi.org/10.1007/s00006-015-0595-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2015 1 30 08 45-57
allfields_unstemmed	10.1007/s00006-015-0595-0 doi (DE-627)SPR000088846 (SPR)s00006-015-0595-0-e DE-627 ger DE-627 rakwb eng Schott, René verfasserin aut Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Classical approaches to routing problems often employ construction of trees and the use of heuristics to prevent combinatorial explosion. The algebraic approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeon algebras. Their inherent combinatorial properties make them useful for routing problems by implicitly pruning the underlying tree structures. Through the use of generalized idempotent algebras, max-min operators can be implemented for non-additive weights. Moreover, these algebras occur as subalgebras of Clifford algebras, lending them a natural connection to quantum probability and (by extension) to quantum computing. Shortest paths (dpeaa)DE-He213 Message routing (dpeaa)DE-He213 Semigroup algebras (dpeaa)DE-He213 Staples, G. Stacey aut Enthalten in Advances in applied Clifford algebras Cham (ZG) : Springer International Publishing AG, 1997 27(2015), 1 vom: 30. Aug., Seite 45-57 (DE-627)507183274 (DE-600)2220151-8 1661-4909 nnns volume:27 year:2015 number:1 day:30 month:08 pages:45-57 https://dx.doi.org/10.1007/s00006-015-0595-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2015 1 30 08 45-57
allfieldsGer	10.1007/s00006-015-0595-0 doi (DE-627)SPR000088846 (SPR)s00006-015-0595-0-e DE-627 ger DE-627 rakwb eng Schott, René verfasserin aut Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Classical approaches to routing problems often employ construction of trees and the use of heuristics to prevent combinatorial explosion. The algebraic approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeon algebras. Their inherent combinatorial properties make them useful for routing problems by implicitly pruning the underlying tree structures. Through the use of generalized idempotent algebras, max-min operators can be implemented for non-additive weights. Moreover, these algebras occur as subalgebras of Clifford algebras, lending them a natural connection to quantum probability and (by extension) to quantum computing. Shortest paths (dpeaa)DE-He213 Message routing (dpeaa)DE-He213 Semigroup algebras (dpeaa)DE-He213 Staples, G. Stacey aut Enthalten in Advances in applied Clifford algebras Cham (ZG) : Springer International Publishing AG, 1997 27(2015), 1 vom: 30. Aug., Seite 45-57 (DE-627)507183274 (DE-600)2220151-8 1661-4909 nnns volume:27 year:2015 number:1 day:30 month:08 pages:45-57 https://dx.doi.org/10.1007/s00006-015-0595-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2015 1 30 08 45-57
allfieldsSound	10.1007/s00006-015-0595-0 doi (DE-627)SPR000088846 (SPR)s00006-015-0595-0-e DE-627 ger DE-627 rakwb eng Schott, René verfasserin aut Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract Classical approaches to routing problems often employ construction of trees and the use of heuristics to prevent combinatorial explosion. The algebraic approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeon algebras. Their inherent combinatorial properties make them useful for routing problems by implicitly pruning the underlying tree structures. Through the use of generalized idempotent algebras, max-min operators can be implemented for non-additive weights. Moreover, these algebras occur as subalgebras of Clifford algebras, lending them a natural connection to quantum probability and (by extension) to quantum computing. Shortest paths (dpeaa)DE-He213 Message routing (dpeaa)DE-He213 Semigroup algebras (dpeaa)DE-He213 Staples, G. Stacey aut Enthalten in Advances in applied Clifford algebras Cham (ZG) : Springer International Publishing AG, 1997 27(2015), 1 vom: 30. Aug., Seite 45-57 (DE-627)507183274 (DE-600)2220151-8 1661-4909 nnns volume:27 year:2015 number:1 day:30 month:08 pages:45-57 https://dx.doi.org/10.1007/s00006-015-0595-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2015 1 30 08 45-57
language	English
source	Enthalten in Advances in applied Clifford algebras 27(2015), 1 vom: 30. Aug., Seite 45-57 volume:27 year:2015 number:1 day:30 month:08 pages:45-57
sourceStr	Enthalten in Advances in applied Clifford algebras 27(2015), 1 vom: 30. Aug., Seite 45-57 volume:27 year:2015 number:1 day:30 month:08 pages:45-57
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Shortest paths Message routing Semigroup algebras
isfreeaccess_bool	false
container_title	Advances in applied Clifford algebras
authorswithroles_txt_mv	Schott, René @@aut@@ Staples, G. Stacey @@aut@@
publishDateDaySort_date	2015-08-30T00:00:00Z
hierarchy_top_id	507183274
id	SPR000088846
language_de	englisch
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author	Schott, René
spellingShingle	Schott, René misc Shortest paths misc Message routing misc Semigroup algebras Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems
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topic_title	Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems Shortest paths (dpeaa)DE-He213 Message routing (dpeaa)DE-He213 Semigroup algebras (dpeaa)DE-He213
topic	misc Shortest paths misc Message routing misc Semigroup algebras
topic_unstemmed	misc Shortest paths misc Message routing misc Semigroup algebras
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title	Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems
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title_full	Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems
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author_browse	Schott, René Staples, G. Stacey
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author-letter	Schott, René
doi_str_mv	10.1007/s00006-015-0595-0
title_sort	generalized zeon algebras: theory and application to multi-constrained path problems
title_auth	Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems
abstract	Abstract Classical approaches to routing problems often employ construction of trees and the use of heuristics to prevent combinatorial explosion. The algebraic approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeon algebras. Their inherent combinatorial properties make them useful for routing problems by implicitly pruning the underlying tree structures. Through the use of generalized idempotent algebras, max-min operators can be implemented for non-additive weights. Moreover, these algebras occur as subalgebras of Clifford algebras, lending them a natural connection to quantum probability and (by extension) to quantum computing. © Springer Basel 2015
abstractGer	Abstract Classical approaches to routing problems often employ construction of trees and the use of heuristics to prevent combinatorial explosion. The algebraic approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeon algebras. Their inherent combinatorial properties make them useful for routing problems by implicitly pruning the underlying tree structures. Through the use of generalized idempotent algebras, max-min operators can be implemented for non-additive weights. Moreover, these algebras occur as subalgebras of Clifford algebras, lending them a natural connection to quantum probability and (by extension) to quantum computing. © Springer Basel 2015
abstract_unstemmed	Abstract Classical approaches to routing problems often employ construction of trees and the use of heuristics to prevent combinatorial explosion. The algebraic approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeon algebras. Their inherent combinatorial properties make them useful for routing problems by implicitly pruning the underlying tree structures. Through the use of generalized idempotent algebras, max-min operators can be implemented for non-additive weights. Moreover, these algebras occur as subalgebras of Clifford algebras, lending them a natural connection to quantum probability and (by extension) to quantum computing. © Springer Basel 2015
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title_short	Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems
url	https://dx.doi.org/10.1007/s00006-015-0595-0
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up_date	2024-07-03T13:54:42.920Z
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