Consider a graph $G(V,E)$. Each edge $e$ has two weights $A_e$ and $B_e$. Find a spanning tree that minimizes the product $\left(\sum_{e \in T}{A_e}\right)\left(\sum_{e \in T}{B_e}\right)$. The algorithm should run in polynomial time with respect to $|V|, |E|$.I find it difficult to adapt any of the traditional algorithms on spanning trees(Kruskal, Prim, Edge-Deletion). How to solve it? Any hints?
Minimal Spanning Tree With Double Weight Parameters
algorithms;graph theory;spanning trees