  We apply our 3D debris disk model, SMACK, to simulate a planet on a circular
orbit near a ring of planetesimals that are experiencing destructive
collisions. Previous simulations of a planet opening a gap in a collisionless
debris disk have found that the width of the gap scales as the planet mass to
the 2/7th power ($\alpha$=2/7). We find that the gap sizes in a collisional
disk still obey a power law scaling with planet mass, but that the index alpha
of the power law depends on the age of the system t relative to the collisional
timescale $t_{coll}$ of the disk by $\alpha = 0.32(t/t_{coll})^{-0.04}$, with
inferred planet masses up to five times smaller than those predicted by the
classical gap law. The increased gap sizes likely stem from the interaction
between the collisions and the mean motion resonances near the chaotic zone. We
investigate the effects of the initial eccentricity distribution of the disk
particles and find a negligible effect on the gap size at Jovian planet masses,
since collisions tend to erase memory of the initial particle eccentricity
distributions. Finally, we find that the presence of Trojan analogs is a
potentially powerful diagnostic of planets in the mass range ~1-10 $M_{jup}$.
We apply our model to place new upper limits on planets around Fomalhaut, HR
4796 A, HD 202628, HD 181327, and $\beta$ Pictoris.
