Interactive Assistive Framework for Maximum Profit Routing in Public Transportation in Smart Cities

Abstract

We design an interactive framework for public transportation route planning in order to maximize the total profit (i.e. revenue minus costs). The framework allows specification of fixed points of interest (urban or tourism), each with a time avalability constraint (in hours), as well as a fleet count of public transportation vehicles. The main contributions of the framework are two approximation algorithms. The first algorithm, based on bin packing, has an approximation ratio of ⋍ 26 log T, where T is a constant denoting the latest deadline (in hours). The second algorithm is based on well-separated pair decompositions and has an approximation ratio of ⋍ 15 log T. While our algorithms may seem to have rather high approximation ratios, in practice they work well and, in the majority of cases, the profit obtained is at least 80% of the optimum. Our framework can be used to simulate the route planning in a Google Maps API environment. The algorithms were tested on a real-world dataset, and we also present the experimental results in this dataset.