We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geo...
Θk-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to...
Nicolas Bonichon, Cyril Gavoille, Nicolas Hanusse,...
We introduce a hierarchical partitioning scheme of the Euclidean plane, called circular partitions. Such a partition consists of a hierarchy of convex polygons, each having small ...
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
We give the first polynomial-time approximation scheme (PTAS) for the Steiner forest problem on planar graphs and, more generally, on graphs of bounded genus. As a first step, w...