Computational geometry is one of the newer branches of computerscience and it has already contributed greatly to the field, not only inthe problems it has given us, but also in new data structures designedfor these problems that have found application in other areas, and innew approaches to problem solving. This paper looks at one of theclassic problems of computational geometry and finds some new twists.The problem is point location in a monotone decomposition of the planewith dynamic updates. A monotone decomposition of the plane is one inwhich the boundary of each polygonal region can be split into two chainssuch that any horizontal line intersects each chain at most once. Theoperations allowed in the updates include adding and deleting new edgesor new chains of edges as well as merging or splitting vertices.

The originality of this work is mainly in its creative combinationof data structures from earlier work into an integrated whole thatsolves this specific problem. Because of this, many of the details areleft for the reader to work out by reading the original sources of theideas. This will not be a problem for the paper’s intendedaudience--other researchers in this area--but may be enough todiscourage others from outside the area from taking a casual look atit.

This is solid research, but likely to be of interest only to othersworking in the area. It is evolutionary, not revolutionary.