We study shortest paths in directed graphs whose edge weights are of the form $$wt(e) = a_{e,1} \lambda_1 + a_{e,2} \lambda_2 + a_{e,3} \lambda_3 + \cdots + a_{e,d} \lambda_d + a_{e,d+1}.$$
Here, each $a_{e,i}\in\mathbb{R}$ is a fixed constant for each edge $e$, whereas each $\lambda_i$ is a shared variable ... more >>>