Ramified Rectilinear Polygons: Coordinatization by Dendrons

Evacuation of Rectilinear Polygons

We investigate the problem of creating fast evacuation plans for buildings that are modeled as grid polygons, possibly containing exponentially many cells. We study this problem in two contexts: the “confluent” context in which the routes to exits remain fixed over time, and the “non-confluent” context in which routes may change. Confluent evacuation plans are simpler to carry out, as they allo...

Competitive Exploration of Rectilinear Polygons

Exploring a polygon with robots when the robots do not have knowledge of the surroundings can be viewed as an online problem. Typical for online problems is that decisions must be made based on past events without complete information about the future. In our case the robots do not have complete information about the environment. Competitive analysis can be used to measure the performance of me...

A note on approximations of rectilinear polygons

Generalized Guarding and Partitioning for Rectilinear Polygons

Extending Rectangle Join Algorithms for Rectilinear Polygons

Spatial joins are very important but costly operations in spatial databases. A typical evaluation strategy of spatial joins is to perform the join on approximations of spatial objects and then evaluate the join of the real objects based on the results. The common approximation is the minimum bounding rectangle. Minimum bounding rectangles are coarse approximations of spatial objects and may cau...