Microscopic models of flocking and swarming takes in account large numbers of
interacting individ- uals. Numerical resolution of large flocks implies huge
computational costs. Typically for N interacting individuals we have a cost
of O(N2). We tackle the problem numerically by considering approximated
binary interaction dynamics described by kinetic equations and simulating such
equations by suitable stochastic methods. This approach permits to compute
approximate solutions as functions of a small scaling parameter ε
at a reduced complexity of O(N) operations. Several numerical results show the
efficiency of the algorithms proposed