Generalizing the ordinary Euclidean Voronoi diagram, the
Voronoi diagram with respect to the Laguerre distance is
proposed.  An \$O(n log n)\$-time divide-and-conquer
algorithm is given.  This diagram can be applied to solve several
problems concerning discs, especially, the problem of computing the
connected components of discs, which has connection with Gershgorin's
theorem in numerical analysis.