An Algorithm for Special Case Shortest Path Problems with Resource Constraints and Time-Based Costs

The Shortest path problem (SPP) has been around for quite a while. Over the years it has seen many variations and extensions. Solutions to any of these problems have proven to be of importance for many practical issues. Perhaps one of the most well-known examples is that of a car's navigational system determining what route to take. Besides the practical implementations the problem can also be used for theoretical purposes. In both the practical and theoretical implementations the time it takes to solve the problem has been essential. In certain instances, it has been proven that in order to solve the problem (to an optimum) an excessive amount of time is required. For such instances we have come to rely on algorithms that sacrifice the quality of the solution in favour of reducing the solving time.