Operator Calculus Algorithms for Multi-Constrained Paths

Abstract : Classical approaches to multi-constrained routing problems gener- ally require construction of trees and the use of heuristics to prevent combinatorial explosion. Introduced here is the notion of constrained path algebras and their application to multi-constrained path prob- lems. The inherent combinatorial properties of these algebras make them useful for routing problems by implicitly pruning the underlying tree structures. Operator calculus (OC) methods are generalized to multiple non-additive constraints in order to develop algorithms for the multi constrained path problem and multi constrained optimiza- tion problem. Theoretical underpinnings are developed first, then algorithms are presented. These algorithms demonstrate the tremen- dous simplicity, flexibility and speed of the OC approach. Algorithmsare implemented in Mathematica and Java and applied to a problem first proposed by Ben Slimane et al. as an example.
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Contributor : Evangelia Tsiontsiou <>
Submitted on : Monday, December 14, 2015 - 11:12:19 AM
Last modification on : Thursday, February 7, 2019 - 5:34:42 PM


  • HAL Id : hal-01242868, version 1



Jamila Ben Slimane, Schott René, Yeqiong Song, G. Stacey Staples, Evangelia Tsiontsiou, et al.. Operator Calculus Algorithms for Multi-Constrained Paths . International Journal of Mathematics and Computer Science, 2015, Vol. 10 ( No. 1). ⟨hal-01242868⟩



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