  In this paper, we consider the problem of finding the maximum routing
throughput between any pair of nodes in an arbitrary multirate wireless mesh
network (WMN) using multiple paths. Multipath routing is an efficient technique
to maximize routing throughput in WMN, however maximizing multipath routing
throughput is a NP-complete problem due to the shared medium for
electromagnetic wave transmission in wireless channel, inducing collision-free
scheduling as part of the optimization problem. In this work, we first provide
problem formulation that incorporates collision-free schedule, and then based
on this formulation we design an algorithm with search pruning that jointly
optimizes paths and transmission schedule. Though suboptimal, compared to the
known optimal single path flow, we demonstrate that an efficient multipath
routing scheme can increase the routing throughput by up to 100% for simple
WMNs.
