Let $\Gamma$ be a non convex set in $R^2$. I would like to know which is the fastest algorithm to divide $\Gamma$ in the minimum number of disjoint convex sets: $$min \;N$$ subject to: $$\Gamma=\underset{i=1,...,N}{\cup}V_i$$
$$V_j\cap V_k=\emptyset\;\;\;\forall j \ne k $$ $$V_i \:\:convex \:\:set \;\; \forall i=1,...,N$$
EDIT: Assume that $\Gamma$ is a rectangle with piecewise linear "holes" (see this figure)
It's also fine if the implementation doesn't get the optimal solution, but a near one: The idea is to solve several path-planning convex optimization problems in real-time (I'm using Gurobi) in each set $V_i$. The smaller N the better, but the more time it takes to compute the sets, the worse.
Thanks!