Summary: | We investigate the ride sharing routing problem from an algorithmic point of view. The research is conducted to the paper `Algorithms for Trip-Vehicle Assignment in Ride-Sharing' by Bei & Zhang, 2018 to find a better algorithm that provides more optimized output in a more efficient time. The objective of the problem is to assign each drivers to fetch two passengers given the locations of drivers, passengers' pick-up points and their destinations. We then designed an algorithm and observed that it produces smaller costs solution in most of the randomly generated data with time complexity $O(n^2\log n)$ for real valued weighted graph and $O(n^2)$ for integer valued weighted graph improved from the previous $O(n^3)$.
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