This paper introduces novel object shape representation using Density Histogram of Feature Points (DHFP). We use silhouette images where the image region ξ consists of only those pixels that correspond to points on the object and have a value one (1) indicating “on” pixels. We count the number of on pixels in a rectangle boundary around the centroid, in the event that there are no “on” pixels i...

Large Alpha-Beta search trees generated by game-playing programs are hard to represent graphically. This paper describes how treemaps can be applied to the visualization of these trees. The principle of treemaps is presented, and difficulties of its application to the particular structure of search trees are reviewed. An original “ordered squarified” layout is proposed. It has been implemented ...

We develop a general strategy in order to implement approximate discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is rectangle equipped with Cartesian grid. For leap-frog scheme, we explain why our provides explicit numerical on four sides and it does not require prescribing any condition at corners ...

We propose in this note a spectral method on triangles based on a new rectangle-to-triangle mapping, which leads to more reasonable grid distributions and efficient implementations than the usual approaches based on the collapsed transform. We present the detailed implementation for spectral approximations on a triangle and discuss the extension to spectral-element methods and three dimensions.

We prove that rectangle-faced orthostacks, a restricted class of orthostacks, can be grid-edge unfolded without additional refinement. We prove several lemmas applicable to larger classes of orthostacks, and construct an example to illustrate that our algorithm does not directly extend to more general classes of orthostacks.

This paper gives some opinions about grid bottleneck problem, and makes some suggestions about grid structure. It also introduces how to construct the global grid with sub grids, and to make use of the advantages of administrative hierarchy. The paper presents the conceptions of static resources, dynamic resources and the ways of scheduling resources. Also, the functions of resource marketplace...

The rectangular grid drawing of a plane graph G is a drawing of G such that each vertex is located on a grid point, each edge is drawn as a horizontal or vertical line segment, and the contour of each face is drawn as a rectangle. In this paper we give a simple linear-time algorithm to find a rectangular grid drawing of G if it exists. We also give an upper bound W + H <~ n /2 on the sum of req...

Pathfinding systems that operate on uniform-cost grid maps are common in the AI literature and application areas such as robotics and real-time video games. Typical speed-up enhancements in such contexts include reducing the size of the search space using abstraction [Botea et al., 2004] and developing new heuristics to more accurately guide search toward the goal [Sturtevant et al., 2009]. Tho...

Finding “good” cycles in graphs is a problem of great interest in graph theory as well as in locational analysis. We show that the center and median problems are NP hard in general graphs. This result holds both for the variable cardinality case (i.e. all cycles of the graph are considered) and the fixed cardinality case (i.e. only cycles with a given cardinality p are feasible). Hence it is of...

The topic of this paper is the rectangle-free coloring of grids using four colors which is equivalent to the edge coloring of complete bipartite graphs without complete monochromatic subgraphs K2,2. So far unsolved are the grids of the sizes 17×17, 17×18, 18×17, and 18×18. The number of different 4-color patterns of the grid 18×18 is equal to 4324 ≈ 1.16798∗10195 . We summarize in this paper so...