A barycentric mapping of a planar graph is a plane embedding in which every internal vertex is the average of its neighbours. A celebrated result of Tutte’s [16] is that if a pl...
We present an algorithm for finding shortest surface non-separating cycles in graphs embedded on surfaces in O(g3/2 V 3/2 log V + g5/2 V 1/2 ) time, where V is the number of vert...
—Over the past few decades, a large family of algorithms—supervised or unsupervised; stemming from statistics or geometry theory—has been designed to provide different soluti...
We show how Embedded Graph Grammars (EGGs) are used to specify local interaction rules between mobile robots in a natural manner. This formalism allows us to treat local network to...
John-Michael McNew, Eric Klavins, Magnus Egerstedt
We give a polynomial-time algorithm to find a shortest contractible cycle (i.e. a closed walk without repeated vertices) in a graph embedded in a surface. This answers a question ...