For determining distances (fetch lengths) from points to polygons in a two-dimensional Euclidean plane, cell-based algorithms provide a simple and effective solution. They divide the input area into a grid of cells that cover the area. The objects are stored into the appropriate cells, and the resulting structure is used for solving the problem. When the input objects are distributed unevenly or the cell size is small, most of the cells may be empty. The representation is then called sparse. In the method proposed in this work, each cell contains information about its distance to the nonempty cells. It is then possible to skip over several empty cells at a time without memory accesses. A cell-based fetch length algorithm is implemented on a graphics processing unit (GPU). Because control flow divergence reduces its performance, several methods to reduce the divergence are studied. While many of the explicit attempts turn out to be unsuccessful, sorting of the input data and sparse traversal are observed to greatly improve performance: compared with the initial GPU implementation, up to 45-fold speedup is reached. The speed improvement is greatest when the map is very sparse and the points are given in a random order.When the number of study points is small, the fetch length problem can be solved simply by iterating over all line segments of the map for every study point and direction, recording the smallest found distances for the study points in the given directions. However, when the number of both study points and line segments of the polygons is large, this method is no longer efficient enough. Most published algorithms for the fetch length problem therefore aim at limiting the number of line segments that need to be examined. The present study also deals with this case where there are numerous study points and line segments.An algorithm that utilizes the tools available in geographical information systems (GIS) has been applied for determining fetch lengths [4,5]. While the algorithm has been described in some detail, it is difficult to determine whether it uses any method for limiting the number of intersection computations; that depends on the operation of the libraries that were used for clipping line segments with polygons.Interval trees [6] and sweep line technique [7] have been used for limiting the number of intersection computations. Both approaches are based on the assumption that the fetch lengths are determined in the same directions for all study points. One can then rotate the map and point data and, after the rotation, determine the lengths in the horizontal direction. Then, for determining the fetch length for a point, the method based on interval trees performs an intersection computation for every line segment that intersects the horizontal line passing through the point. The sweep line method restricts the number of intersection computations further by keeping the line segments sorted in the horizontal direction. For a given study point, it is then only necessary to perform the intersection...