In this paper, the extended finite element method (XFEM) is employed to investigate the statics and vibration problems of cracked isotropic bars and beams. Three kinds of elements namely the standard, the blended and the enriched elements are utilized to discretize the structure and model cracks. Two techniques referred as the increase of the number of Gauss integration points and the rectangle...

In the weighted rectangle stabbing problem we are given a grid in ]R2 consisting of columns and rows each having a positive integral weight, and a set of closed axis-parallel rectangles each having a positive integral demand. The rectangles are placed arbitrarily in the grid with the only assumption that each rectangle is intersected by at least one column and at least one row. The objective is...

A set of rectangles S is said to be grid packed if there exists a rectangular grid (not necessarily regular) such that every rectangle lies in the grid and there is at most one rectangle of S in each cell. The area of a grid packing is the area of a minimal bounding box that contains all the rectangles in the grid packing. We present an approximation algorithm that given a set S of rectangles a...

A set of rectangles S is said to be grid packed if there exists a rectangular grid (not necessarily regular) such that every rectangle lies in the grid and there is at most one rectangle of S in each cell. The area of a grid packing is the area of a minimal bounding box that contains all the rectangles in the grid packing. We present an approximation algorithm that given a set S of rectangles a...

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles, removing from each rectangle all interior nodes and possibly some from along the perimeter. We then add a series of macro-edges between selected pairs of remain...

The robot localization problem requires a mobile robot to determine its current location in an environment, given some initial information about the environment. We assume that the robot’s environment is represented by an occupancy grid. The grid is a rectangle of square cells, each of which is either obstructed or unobstructed. All the edge cells of the rectangle are obstructed. The robot can ...

Grid computing is emerging as a new paradigm for solving large-scale problems and is becoming an established technology for providing transparent access to large-scale distributed computational resources. Resource allocation and application scheduling are two of the most important aspects of Grid computing. In general, a grid application also requires datasets that may not be available at the l...

A rectangle-of-in uence drawing of a plane graph G is a straight-line planar drawing of G such that there is no vertex in the proper inside of the axis-parallel rectangle de ned by the two ends of any edge. In this paper, we show that any 4-connected plane graph G with four or more vertices on the outer face has a rectangle-of-in uence drawing in an integer grid such that W + H n, where n is th...

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. Despite a strong mathematical background it is not known whether rectangle-free 4-colorable grids exist for five large grid sizes. We present in this paper an approach that solves the most complex p...