  In this paper, we address pursuit-evasion problems involving multiple
pursuers and multiple evaders. The pursuer and the evader teams are assumed to
be heterogeneous, in the sense that each team has agents with different speed
capabilities. The pursuers are all assumed to be following a constant bearing
strategy. A dynamic divide and conquer approach, where at every time instant
each evader is assigned to a set of pursuers based on the instantaneous
positions of all the players, is introduced to solve the multi-agent pursuit
problem. In this regard, the corresponding multi-pursuer single-evader problem
is analyzed first. Assuming that the evader can follow any strategy, a dynamic
task allocation algorithm is proposed for the pursuers. The algorithm is based
on the well-known Apollonius circle and allows the pursuers to allocate their
resources in an intelligent manner while guaranteeing the capture of the evader
in minimum time. The proposed algorithm is then extended to assign pursuers in
multi-evader settings that is proven to capture all the evaders in finite time.
