Generalized zeon algebras: theory and application to multi-constrained path problems

René Schott (1, 2) , George Stacey Staples (3)

1 IECL - Institut Élie Cartan de Lorraine
2 LORIA - NSS - Department of Networks, Systems and Services
3 Department of Mathematics and Statistics - Southern Illinois University

Classical approaches to routing problems invariably require construction of trees and the use of heuristics to prevent combinatorial explosion. The operator calculus approach presented herein, however, allows such explicit tree constructions to be avoided. Introduced here is the notion of generalized zeon algebras and their associated operator calculus. The inherent combinatorial properties of generalized zeons make them useful for routing problems by implicitly pruning the underlying tree structures. As an application, an operator calculus approach to multi-constrained path problems is described.

Mots clés: operator calculus; semigroup algebras; shortest paths; message routing

Domaines: Probabilités [math.PR]

René Schott, George Stacey Staples. Generalized zeon algebras: theory and application to multi-constrained path problems. Advances in Applied Clifford Algebras, 2017, 27 (1), pp.45-57. ⟨10.1007/s00006-015-0595-0⟩. ⟨hal-00603748⟩