We explore a symmetry-based reformulation technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by over 30 times. Our offline approach decomposes grid maps into a set of empty rectangles, removing from each all interior nodes and possibly some from along the perimeter. We then add macro-edges between selected pairs of remaining perimeter nodes to facilitate prova...

In this paper, we propose a new branch and bound algorithm for the solution of large scale separable concave programming problems. The largest distance bisection (LDB) technique is proposed to divide rectangle into sub-rectangles when one problem is branched into two subproblems. It is proved that the LDB method is a normal rectangle subdivision(NRS). Numerical tests on problems with dimensions...

_______________________________ In this paper, we present the geospatial methods in conjunction with results of a newly developed storm surge and sub-grid inundation model which was applied in New York City during Hurricane Sandy in 2012. Sub-grid modeling takes a novel approach for partial wetting and drying within grid cells, eschewing the conventional hydrodynamic modeling method by nesting ...

We present the first subquadratic algorithms for computing similarity between a pair of point sequences in R, for any fixed d > 1, using dynamic time warping (DTW) and edit distance, assuming that the point sequences are drawn from certain natural families of curves. In particular, our algorithms compute (1 + ε)-approximations of DTW and ED in near-linear time for point sequences drawn from κ-p...

The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor co. We show that, for the standard model problem of Poisson's equation on a rectangle, the optimal co and corresponding convergence rate can be obtained rigorously by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives new...

The use of bounding structures in the form of orthogonal polygons (also known as rectilinear polygons) with a varying number of vertices in contrast with a minimum bounding rectangle (an orthogonal polygon with just 4 vertices in two dimensions) as an object approximation method is presented. Orthogonal polygons can be used to improve the performance of the re ne step in the lterre ne query pro...

A c-coloring of the grid GN,M = [N] × [M] is a mapping into [c] such that no four corners forming rectangle have same color. In 2009 challenge was proposed to find 4-coloring G17,17. Though coloring produced, finding it proved be difficult. This raises question whether there some complexity lower bound. Consider following problem: given partial grid, can extended full c-coloring? We show this p...

We implement the Predicting Particles Produced in Power-Plant Plumes (P6) sub-grid sulphate parameterization for the first time into a global chemical-transport model with online aerosol microphysics, the GEOS-Chem-TOMAS model. Compared to simulations using two other previous treatments of sub-grid sulphate, simulations using P6 subgrid sulphate predicted similar or smaller increases (depending...

Some discrete models for a simplified (compared to that published earlier in JODEA, 28 (1) (2020), 1 – 42) initial boundary value problem 1D linear degenerate wave equation, posed space-time rectangle and solved exactly (JODEA, 30 (2022), 89 121), have been considered. It has demonstrated the correct evaluation of grid flux can be possible.