We are interested in Voronoi diagrams as a tool in robot path planning, where the search for a path in an r-dimensional space may be simplified to a search on an (r- l)-dimensional...
We revisit one of the most fundamental classes of data structure problems in computational geometry: range searching. Back in SoCG’92, Matouˇsek gave a partition tree method fo...
Abstract. We show that many so called discrete weak semilattices considered earlier in a series of author’s publications have hereditary undecidable first-order theories. Since ...
We present SNAP (Small-world Network Analysis and Partitioning), an open-source graph framework for exploratory study and partitioning of large-scale networks. To illustrate the c...
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular g...