Unlike the shortest paths problem which admits efficient polynomial time algorithms, the longest paths problem in graphs is NPhard with no known polynomial time algorithms. The longest paths problem comes in many variants:

Solution: the categorization of functional and non-functional requirement are as follows: some of the more typical functional requirements include: • business rules• transaction corrections, adjustments and cancellations• administrative functions• authentication• authorization levels• audit tracking• external interfaces• certification requirements• reporting requirements• historical data• legal or regulatory requirementswhile,some typical non-functional requirements are: • performance – for example response time, throughput, utilization, static volumetric• scalability• capacity• availability• reliability• recoverability• maintainability• serviceability• security• regulatory• manageability• environmental• data integrity• usability• interoperability

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