This paper introduces a near-linear time sequential algorithm for constructing a sparse neighborhood cover. This implies analogous improvements (from quadratic to near-linear time)...
Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [14]. However, for graphs of treewidth larger than ...
Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclid...
Given an unweighted planar graph G together with nets of terminals, our problem is to find a Steiner forest, i.e., vertex-disjoint trees, each of which interconnects all the termin...
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...