  Typical vertex finding algorithms use reconstructed tracks, registered in a
multi-layer detector, which directly point to the common point of origin. A
detector with a single layer of silicon sensors registers the passage of
primary particles only in one place. Nevertheless, the information available
from these hits can also be used to estimate the vertex position, when the
geometrical properties of silicon sensors and the measured ionization energy
losses of the particles are fully exploited. In this paper the algorithm used
for this purpose in the PHOBOS experiment is described. The vertex
reconstruction performance is studied using simulations and compared with
results obtained from real data. The very large acceptance of a single-layered
multiplicity detector permits vertex reconstruction for low multiplicity events
where other methods, using small acceptance subdetectors, fail because of
insufficient number of registered primary tracks.
