The results in this paper are closely related to the effective use of the divide-and-conquer strategy for solving problems on planar graphs. It is shown that every planar graph can be partitioned… Expand

If G is an n vertex maximal planar graph and δ≤1 3, then the vertex set of G can be partitioned into three sets A, B, C such that neither A nor B has weight exceeding 1−δ, and C is a simple cycle with no more than 2√n+O(1) vertices.Expand

We show that the Voronoi diagram of a finite sequence of points in the plane which gives sorted order of the points with respect to two perpendicular directions can be computed in linear time. In… Expand

This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional.Expand

It is proved that the bisection width of the class of planar graphs and trees of n vertices and maximum degree k is O ([formula] and O ( k log n /log k ), respectively, both optimal within a constant factor.Expand

This paper develops new techniques for constructing separators for graphs embedded on surfaces of bounded genus and shows that any arbitrarily small positive graph G of genus g can be divided in O(n+g) time into components whose sizes do not exceed $\varepsilon n$ by removing a set of $C$ of $O(\sqrt{(g+1/\varePSilon)n})$ vertices.Expand

It is shown that, if G is an n-vertex graph of maximum degree d and orientable genus g, then there exists a planarizing set of O(√dgn) edges that can be found in O(n+g) time, if an embedding of G on a surface of genus g is given.Expand

A single-source query data structure SSQ(a;P,ε) that can answer ε-approximate distance queries from a fixed point a to any query point on P in logarithmic time is developed and based on a novel graph separator algorithm introduced and analyzed here.Expand

An algorithm for imbedding a graph G of n vertices onto an oriented surface of minimal genus g is given and a “bootstrap” technique is used that uses a discovered forbidden subgraph for given genus g'<g to aid us in determination of genus g’+1 imbeddings.Expand

A model is a simple set of analytical functions that predict the execution time of the generated code and is able to predict tile sizes that achieve a further improvement of 9% on average, and is experimentally validate on a number of stencil codes.Expand