A Look at Algorithm BEPtoPNST

Abstract

This work analyzes the computational complexity of algorithm BEPtoPNST which transforms a building-evacuation problem (BEP) into a time-ex-panded, process-network synthesis (PNST) 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 BEPtoPNST 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 (2h)) in the worst case; where h represents the total number of operating units specified in the corresponding PNST problem. Nevertheless, the computational comple-xity can be reduced significantly when the P-graph method is deployed.