We study the Integer-weighted Grid All Paths Scores (IGAPS) problem, which is given a grid graph, to compute the maximum weights of paths between every pair of a vertex on the first row of the graph and a vertex on the last row of the graph. We also consider a variant of this problem, periodic IGAPS, where the input grid graph is periodic and infinite. For these problems, we consider both the g...

Bidimensionality is a powerful tool for developing subexponential fixed-parameter algorithms for combinatorial optimization problems on graph families that exclude a minor. This paper completes the theory of bidimensionality for graphs of bounded genus (which is a minorexcluding family). Specifically we show that, for any problem whose solution value does not increase under contractions and who...

Pattern recognition is an important step in map generalization. Pattern recognition in street network is significant for street network generalization. A grid is characterized by a set of mostly parallel lines, which are crossed by a second set of parallel lines with roughly right angle. Inspired by object recognition in image processing, this paper presents an approach to the grid recognition ...

Treedepth is a well-studied graph invariant in the family of “width measures” that includes treewidth and pathwidth. Understanding these invariants in terms of excluded minors has been an active area of research. The recent Grid Minor Theorem of Chekuri and Chuzhoy [12] establishes that treewidth is polynomially approximated by the largest k×k grid minor. In this paper, we give a similar polyno...

This paper studies the problem of computing 3D crossing-free straight-line grid drawings of graphs such that the overall volume is small. We show that every 2-tree (and therefore every series-parallel graph) can be drawn on an integer 3D grid consisting of 15 parallel lines and having linear volume. We extend the study to the problem of drawing general k-trees on a set of parallel grid lines. L...

Given a plane graph G, we wish to draw it in the plane in such a way that the vertices of G are represented as grid points, and the edges are represented as straight-line segments between their endpoints. An additional objective is to minimize the size of the resulting grid. It is known that each plane graph can be drawn in such a way in an (n 2) x (n 2) grid (for n ~> 3), and that no grid smal...

A major component of computer chip design is creating an optimal physical layout of a netlist, i.e., determining where to place the functional elements and how to route the wires connecting them when manufacturing a chip. Because of its basic structure, the overall problem of netlist layout contains many questions that lend themselves to graph theoretical modeling and analysis. We will describe...

This paper describes a novel procedure based on Core Path Graphs to generate continuously differentiable sub-optimal paths for wheeled mobile robots in the presence of obstacles. The operational scenario is first discretized with a finite dimensional grid of positions-directions pairs. A weighted and oriented graph is then defined whose nodes are the above mentioned grid points, and whose arcs ...

Let G be a class of graphs. A d-fold grid over G is a graph obtained from a d-dimensional rectangular grid of vertices by placing a graph from G on each of the lines parallel to one of the axes. Thus each vertex belongs to d of these subgraphs. The class of d-fold grids over G is denoted by Gd. Let f(G; d) = maxG∈Gd χ(G). If each graph in G is k-colorable, then f(G; d) ≤ kd. We show that this b...