Solutions to constrained linear model predictive. control problems can be precomputed;offline in an explicit form as a piecewise linear state feedback on a polyhedral partition of the state-space, avoiding real-time optimization., We suggest an algorithm that will determine an approximate explicit piecewise linear state feedback by imposing an orthogonal search tree structure on the partition. This leads to. a real-time computational complexity that is logarithmic in the number of regions in the partition, and the algorithm yields guarantees on the suboptimality, asymptotic stability and constraint fulfillment.