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Map labeling is of fundamental importance in cartography and geographical information systems and is one of the areas targeted for research by the ACM Computational Geometry Impact Task Force. Previous work on map labeling has focused on the problem of placing maximal uniform, axis-aligned, disjoint rectangles on the plane so that each point feature to be… (More)

We consider the robot exploration problem of graph maps with homogeneous markers, following the graph world model introduced by Dudek et al. DJMW]. The environment is a graph consisting of nodes and edges, where the robot can navigate from one node to another through an edge connecting these two nodes. However, the robot may not distinguish one node (or… (More)

A mobile robot often executes a planned path by measuring its position relative to visible landmarks at known positions and then using this information to estimate its own absolute position. The minimum number of landmarks k required for self-location depends on the types of measurements the robot can perform, such as visual angles using a video camera on a… (More)

Let Σ ={S 1 , ... , S n }beafinite set of disjoint line segments in the plane. Wec onjecture that its visibility graph, Vis(Σ), is hamiltonian. In fact, we maket he stronger conjecture that Vis(Σ)h as a hamiltonian cycle whose embedded version is a simple polygon (i.e., its boundary edges are non-crossing visibility segments). Wec all such a simple polygon… (More)