Advances in Applied Clifford Algebras

, Volume 27, Issue 1, pp 45–57 | Cite as

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

Article

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.

Keywords

Shortest paths Message routing Semigroup algebras 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.IECN and LORIAUniversité de LorraineVandoeuvre-lès-NancyFrance
  2. 2.Department of Mathematics and StatisticsSouthern Illinois University EdwardsvilleEdwardsvilleUSA

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