We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given...
We give an algorithm to morph between two planar drawings of a graph, preserving planarity, but allowing edges to bend. The morph uses a polynomial number of elementary steps, whe...
The disk dimension of a planar graph G is the least number k for which G embeds in the plane minus k open disks, with every vertex on the boundary of some disk. Useful properties ...
Double Patterning Lithography (DPL) is one of the few hopeful candidate solutions for the lithography for CMOS process beyond 45nm. DPL assigns the patterns less than a certain di...
We present a new algorithm that enables a convex shaped robot to explore an unknown planar workspace, i.e., an unknown configuration space diffeomorphic to SE(2). This new algor...