Abstract

GARCIA-OJEDA, Juan C.. A Look at Algorithm BEPtoPNST. Rev. ing. univ. Medellín [online]. 2021, vol.20, n.39, pp.115-128.  Epub June 28, 2022. ISSN 1692-3324.  https://doi.org/10.22395/rium.v20n39a7.

This work analyzes the computational complexity of algorithm BEPtoPNS T which transforms a building-evacuation problem (BEP) into a time-expanded, process-network synthesis (PNS T ) problem. The solution of the latter is achieved by resorting to the P-graph method which exploits the combinatorial nature of a BEP. Unlike other approaches, the P-graph method provides not only the optimal solution (best evacuation route as a function of egress time), but also the best n sub-optimal solutions. For the complexity analysis, a generic processor, and a Random-access machine (RAM) model were deployed as well as a mathematical model to calculate the number and cost of the operations performed. It was observed that algorithm BEPtoPNS T exhibits an asymptotic complexity of order O ( T | A | (| N | -k)). When solving a BEP, however, the total complexity grows exponentially with order O (T | A | (| N | -k)) + O (2 h )) in the worst case; where h represents the total number of operating units specified in the corresponding PNS T problem. Nevertheless, the computational complexity can be reduced significantly when the P-graph method is deployed.

Keywords : building-evacuation routes; process-network synthesis; rigorous structures; combinatorial optimization; P-graph; pseudocode; RAM model; algorithm complexity; asymptotic notation; Big-O.

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