In this paper, we derive a topological pattern of urban street networks using a large sample (the largest so far to the best of our knowledge) of 40 US cities and a few more from elsewhere of different sizes. It is found that all the topologies of urban street networks based on street–street intersection demonstrate a small world structure, and a scale-free property for both street length and c...

Given a directed graph G = (N,A), a tension is a function from A to R which satisfies Kirchhoff’s law for voltages. There are two well-known tension problems on graphs. In the minimum cost tension problem (MCT), a cost vector is given and a tension satisfying lower and upper bounds is seeked such that the total cost is minimum. In the maximum tension problem (MaxT), the graph contains 2 special...

In this paper, an O ( n log log n ) algorithm is proposed for minimally rectangular partitioning a simple rectilinear polygon. For any simple rectilinear polygon P , a vertex-edge visible pair is a vertex and an edge that can be connected by a horizontal or vertical line segment that lies entirely inside P . We show that, if the vertex-edge visible pairs are found, the maximum matching and the ...

The urban street network is one of the most permanent features of cities. Once laid down, the pattern of streets determines urban form and the level of sprawl for decades to come. We present a high-resolution time series of urban sprawl, as measured through street network connectivity, in the United States from 1920 to 2012. Sprawl started well before private car ownership was dominant and grew...

In a rectilinear drawing of a simple graph G each vertex is mapped to a distinct point in the plane and each edge is represented by a straight-line segment with appropriate ends. The goal of rectilinear crossing minimization is to find a rectilinear drawing of G with as few edge crossings as possible. A new approach to rectilinear crossing minimization is presented including a formulation of th...

We consider the generalized minimum Manhattan network problem (GMMN). The input to this problem is a set R of n pairs of terminals, which are points in R. The goal is to find a minimum-length rectilinear network that connects every pair in R by a Manhattan path, that is, a path of axis-parallel line segments whose total length equals the pair’s Manhattan distance. This problem is a generalizati...

Spatial joins are very important but costly operations in spatial databases. A typical evaluation strategy of spatial joins is to perform the join on approximations of spatial objects and then evaluate the join of the real objects based on the results. The common approximation is the minimum bounding rectangle. Minimum bounding rectangles are coarse approximations of spatial objects and may cau...

A rectilinear Steiner tree for a set T of points in the plane is a tree which connects T using horizontal and vertical lines, In the Rectilinear Steiner Tree problem, input is a set T of n points in the Euclidean plane (R) and the goal is to find an rectilinear Steiner tree for T of smallest possible total length. A rectilinear Steiner arborecence for a set T of points and root r ∈ T is a recti...

Mental representations of spatial knowledge are organized hierarchically. Among people familiar with an urban environment, common spatial knowledge from these spatial mental representations enables successful communication of place and route descriptions, consisting of hierarchically-ordered references to prominent spatial features, such as streets. The more prominent a street is, the more like...