Factorization of Constrained Energy K-Network Reliability with Perfect Nodes

TL;DR

This paper introduces a new factorization theorem for constrained energy K-network reliability, enabling parallel processing to efficiently compute an NP-hard problem and proposing a novel reliability definition.

Contribution

It presents a general factorization theorem for constrained energy reliability and a new reliability definition facilitating parallel computation.

Findings

Theorem enables parallel processing in reliability calculations.

New formula simplifies the calculation of constrained energy reliability.

Proposed definition allows for efficient computation of NP-hard problems.

Abstract

This paper proves a new general K-network constrained energy reliability global factorization theorem. As in the unconstrained case, beside its theoretical mathematical importance the theorem shows how to do parallel processing in exact network constrained energy reliability calculations in order to reduce the processing time of this NP-hard problem. Followed by a new simple factorization formula for its calculation, we propose a new definition of constrained energy network reliability motivated by the factorization theorem and the accomplishment of parallel processing, something impossible with the original definition.