Although its effectiveness (or cost-effectiveness) remains debated, connecting habitat remnants through conservation corridors is an approach to mitigate negative effects of wildlife habitat loss and fragmentation on biodiversity. However, multiple subjective and uncertain factors are often involved in conservation corridor planning and decision-making, ranging from environmental and economic to social and political. These can limit corridor continuity, leading to corridors consisting of isolated habitat fragments that act as “stepping stones” for species movement. To provide computational support for planning such “stepping stones” corridors, we design and implement a raster-based GIS model that characterizes and searches for an optimal sequence of isolated patches across a mosaic of land cover types. The model is unique in two key aspects. First, it simultaneously selects the stepping stones and a path traversing them, which collectively form a corridor. This representation is useful for spatial planning actions engaging organisms to follow a corridor, such as identifying locations for planting or restoration. Second, unlike existing least-cost path models, no quantification of land cover types in terms of suitability (or cost) is required; their rank-ordering is used instead. While subjectivity and uncertainty may remain, they are substantially reduced. We apply the model to a conservation project in Rwanda aimed at enhancing connectivity between two national parks through the establishment of a hedgerow of native plants supporting pollinator birds’ dispersal. The results suggest that the model enables rapid initial delineation of candidate routes for stepping stone corridors and facilitates early exploratory stages of conservation planning.

Accessibility is an essential consideration in the design of public spaces, and commonly referred to as ‘pedestrian accessibility’ when walking is the primary mode of transportation. Computational methods, frequently coupled with Geographic Information systems (GIS), are increasingly available for assessing pedestrian accessibility using digital cartographic data such as road networks and digital terrain models. However, they often implicitly assume a level of mobility that may not be achievable by individuals with mobility impairments, e.g., wheelchair users. Therefore, it remains uncertain whether conventional pedestrian accessibility adequately approximates ‘wheelchair accessibility,’ and, if not, what computational resources would be required to evaluate it more accurately. We therefore designed a spatial database aimed at customizing mobility networks according to mobility limitations and compared the accessibility of a university campus for people with and without wheelchairs under various assumptions. The results showed there are clusters of locations either completely inaccessible or substantially less accessible for wheelchair users, indicating the presence of particular ‘wheelchair coldspots’, not only due to steep slopes and stairways but also arising from unforeseen consequences of aesthetic and safety enhancements, such as pebble pavements and raised sidewalks. It was found that a combination of simple spatial queries would help identifying potential locations for mobility aids such as ramps. These findings suggest that accessibility is not an invariant of a public space but experienced differently by different groups. Therefore, more comprehensive needs analysis and spatial database design are necessary to support inclusive design of healthier public spaces.

Given a grid of cells, each of which is assigned a numerical value quantifying its suitability for a certain use, one problem in geographic information science concerns the selection of a region, i.e. a connected set of cells, with a specified size that maximizes the sum of all their values. This task can be cast as a combinatorial optimization problem called the maximum value region problem, and exact and heuristic methods exist for its solution. While those solutions are guaranteed to be feasible (if not optimal), they may not be desirable for practical use if they contain too narrow segments (down to the width of a single cell). In this paper, we present a new variation of the maximum value region problem—the maximum value wide region problem—that requires a region to be at least as wide as a specified width. We offer a heuristic method for its solution which models a region as a set of neighborhoods and test its performance through computational experiments. Results demonstrate that the method generates good feasible solutions in terms of connectedness, size, width, and value, but requires more computing time than methods for maximum value regions without minimum width requirements.

The least-cost path problem is a widely studied problems in geographic information science. In raster space, the problem is to find a path that accumulates the least amount of cost between two locations based on the assumptions that the path is a one-dimensional object (represented by a string of cells) and that the cost (per unit length) is measured on a quantitative scale. Efficient methods are available for solution of this problem when at least one of these assumptions is upheld. This is not the case when the path has a width and is a two-dimensional object called a corridor (represented by a swath of cells) and the cost (per unit area) is measured on an ordinal scale. In this paper, we propose one additional model that characterizes a least-cost corridor on an ordinal-scaled raster cost surface–or a least ordinal-scaled cost corridor for short–and show that it can be transformed into an instance of a multiobjective optimization problem known as the preferred path problem with a lexicographic preference relation and solved accordingly. The model is tested through computational experiments with artificial landscape data as well as real-world data. Results show that least ordinal-scaled cost corridors are guaranteed to contain smaller areas of higher cost than conventional least-cost corridors at the expense of more elongated and winding forms. The least ordinal-scaled cost corridor problem has computational complexity of O(n 2.5) in the worst case, resulting in a longer computational time than least-cost corridors. However, this difference is smaller in practice.

Optimal routing of a path with a constant width in a two-dimensional grid of cost-weighted square cells or pixels is a recent extension of the least-cost path problem, and models and solutions are available and ready to be integrated into raster-based geographic information systems. In this article we consider yet another variation of this problem in a three-dimensional grid of cost-weighted cubic cells or voxels, which is to find a tubular region of voxels with a constant width, referred to here as “corridor,” connecting two termini while accumulating the least amount of cost. We model a corridor as a sequence of sets of voxels, called “neighborhoods,” that are arranged in a 26-hedral form, design a heuristic method to find a sequence of such neighborhoods that sweeps the minimum cost-weighted volume, and test its performance with computer-generated random data. Results show that the method finds a low-cost, if not least-cost, corridor with a specified width in a three-dimensional cost grid and has a reasonable efficiency as its complexity is O(n2), where n is the number of voxels in the input cost grid and is independent of corridor width. A major drawback is that the corridor found may self-intersect, which often not only is an undesirable quality but also makes the estimation of its cost-weighted volume inaccurate.

Given a grid of cells, each having a value indicating its cost per unit area, a variant of the least-cost path problem is to find a corridor of a specified width connecting two termini such that its cost-weighted area is minimized. A computationally efficient method exists for finding such corridors, but as is the case with conventional raster-based least-cost paths, their incremental orientations are limited to a fixed number of (typically eight orthogonal and diagonal) directions, and therefore, regardless of the grid resolution, they tend to deviate from those conceivable on the Euclidean plane. In this paper, we propose a method for solving the raster-based least-cost corridor problem with reduced distortion by adapting a distortion reduction technique originally designed for least-cost paths and applying it to an efficient but distortion-prone least-cost corridor algorithm. The proposed method is, in theory, guaranteed to generate no less accurate solutions than the existing one in polynomial time and, in practice, expected to generate more accurate solutions, as demonstrated experimentally using synthetic and real-world data.

Selection of optimal paths or sequences of cells from a grid of cells is one of the most basic functions of raster-based geographic information systems. For this function to work, it is often assumed that the optimality of a path can be evaluated by the sum of the weighted lengths of all its segments–weighted, i.e. by the underlying cell values. The validity of this assumption must be questioned, however, if those values are measured on a scale that does not permit arithmetic operations. Through computational experiments with randomly generated artificial landscapes, this paper compares two models, minisum and minimax path models, which aggregate the values of the cells associated with a path using the sum function and the maximum function, respectively. Results suggest that the minisum path model is effective if the path search can be translated into the conventional least-cost path problem, which aims to find a path with the minimum cost-weighted length between two terminuses on a ratio-scaled raster cost surface. On the other hand, the minimax path model is found mathematically sounder if the cost values are measured on an ordinal scale and practically useful if the problem is concerned not with the minimization of cost but with the maximization of some desirable condition such as suitability.

Connectivity is an important landscape attribute in ecological studies and conservation practices and is often expressed in terms of effective distance. If the cost of movement of an organism over a landscape is effectively represented by a raster surface, effective distances can be equated with the cost-weighted distance of least-cost paths. It is generally recognized that this measure is sensitive to the grid's cell size, but little is known if it is always sensitive in the same way and to the same degree and if not, what makes it more (or less) sensitive. We conducted computational experiments with both synthetic and real landscape data, in which we generated and analyzed large samples of effective distances measured on cost surfaces of varying cell sizes derived from those data. The particular focus was on the statistical behavior of the ratio-referred to as 'accuracy indicator'-of the effective distance measured on a lower-resolution cost surface to that measured on a higher-resolution cost surface. Results In the experiment with synthetic cost surfaces, the sample values of the accuracy indicator were generally clustered around 1, but slightly greater with the absence of linear sequences (or barriers) of high-cost or inadmissible cells and smaller with the presence of such sequences. The latter tendency was more dominant, and both tendencies became more pronounced as the difference between the spatial resolutions of the associated cost surfaces increased. When two real satellite images (of different resolutions with fairly large discrepancies) were used as the basis of cost estimation, the variation of the accuracy indicator was found to be substantially large in the vicinity (1500 m) of the source but decreases quickly with an increase in distance from it. Conclusions Effective distances measured on lower-resolution cost surfaces are generally highly correlated with-and useful predictors of-effective distances measured on higher-resolution cost surfaces. This relationship tends to be weakened when linear barriers to dispersal (e.g., roads and rivers) exist, but strengthened when moving away from sources of dispersal and/or when linear barriers (if any) are detected by other presumably more accessible and affordable sources such as vector line data. Thus, if benefits of high-resolution data are not likely to substantially outweigh their costs, the use of lower resolution data is worth considering as a cost-effective alternative in the application of least-cost path modeling to landscape connectivity analysis.

Planners who are involved in locational decision-making often useraster-based geographic information systems to quantify the valueof land in terms of suitability or cost for a certain use. From acomputational point of view, this process can be seen as a transformationof one or more sets of values associated with a grid ofcells into another set of such values through a function reflectingone or more criteria. While it is generally anticipated that differenttransformations lead to different ‘best’ locations, little has beenknown on how such differences arise (or do not arise). The paperattempts to answer this question in the context of path planningthrough a series of computational experiments using a number ofrandom landscape grids with a variety of spatial and nonspatialstructures. In the experiments, we generated least-cost paths on anumber of cost grids transformed from the landscape grids usinga variety of transformation parameters and analyzed the locationsand (weighted) lengths of those paths. Results show that the samepair of terminal cells may well be connected by different least-costpaths on different cost grids though derived from the same landscapegrid and that the variation among those paths is affected byhow given values are distributed in the landscape grid as well asby how derived values are distributed in the cost grids. Mostsignificantly, the variation tends to be smaller when the landscapegrid contains more distinct patches of cells potentially attractingor distracting cost-saving passage or when the cost grid contains asmaller number of low-cost cells.

Selection of optimal paths from a grid of cells is one of the most basicfunctions of raster-based GIS. For this function to work, it is often assumedthat the optimality of a path can be evaluated by the sum of the weightedlengths of all its segments—weighted, i.e., by values of an attributecharacterizing each cell of the grid. The validity of this assumption must bequestioned, however, if the attribute is measured on a scale that does notpermit arithmetic operations. Through a series of computationalexperiments with artificial raster surfaces, this paper compares twomodels, minisum and minimax (or maximin) models, which aggregate a setof cell values associated with a path using the sum and maximum (orminimum) functions, respectively. Results suggest that the minisum modelis effective if the path search can be translated into the conventional leastcostpath problem, which aims to find a path with the minimum costweightedlength between two terminuses on a ratio-scaled raster costsurface, but the minimax (or maximin) model is mathematically sounder ifcost values are measured on an ordinal scale and practically useful if theproblem is concerned not with the minimization of cost but with themaximization of some desirable condition such as suitability.