Group chase and escape with some fast chasers.

We study group chase and escape with some fast chasers. In our model chasers look for the nearest target and move to one of the nearest sites in order to catch the target. On the other hand, targets try to escape from the nearest chaser. When a chaser catches a target, the target is removed from the system and the number of targets decreases. The lifetime of targets, at which all targets caught, decreases as t^{α} with increasing the number of chasers. When there are no fast chasers and the total number of chasers is small, the exponent α is large. When the total number of chasers is large, α becomes small. There is an optimal number of chasers to minimize the cost used in order to catch all targets. However, when we add a few fast chasers, the region with the large α vanishes. The optimal number of chasers vanishes, and the cost monotonically increases with increasing the number of chasers.