Finding minimum loss path in big networks

In this paper, a directed network in which there is a specific percentage of loss for each arc is considered. These losses are due to evaporation, leaks, energy dissipation, theft, etc. We deal with the problem of finding the directed path from a given source node s to a given sink node t that has the minimum loss among all directed paths from s to t. We show how Dijkstra's algorithm can be adapted to deal with this problem. Then, we consider the more general case when on some arcs there is the possibility to have a gain, instead of loss. For solving the latter problem, we adapt Bellman-Ford's algorithm. Since the applicability of these problems is for big networks such as national or international transportation networks of water, gas, electricity, etc., we also study how CPU or GPU parallelization can be applied to the proposed algorithms. The speed-up results are presented and discussed for different networks having various sizes.