  Motion planning is an important and well-studied field of robotics. A typical
approach to finding a route is to construct a {\em cell graph} representing a
scene and then to find a path in such a graph. In this paper we present and
analyze parallel algorithms for constructing the cell graph on a SIMD-like GPU
processor.
  Additionally, we present a new implementation of the dictionary data type on
a GPU device. In the contrary to hash tables, which are common in GPU
algorithms, it uses a search tree in which all values are kept in leaves. With
such a structure we can effectively perform dictionary operations on a set of
long vectors over a limited alphabet.
