Centrality measures define the relationship between particular structural features of a network. Although network analysis has been utilized to express the most relevant physical, topological and static properties of networks, dynamic and temporal aspects are mostly disregarded. For example, in travel network studies the physical street network is assumed to be static, although it can have rele...

We consider the problem of finding a shortest rectilinear Steiner tree for a given set of points in the plane in the presence of rectilinear obstacles that must be avoided. We extend the Steiner ratio to the obstacle-avoiding case and show that it is equal to the Steiner ratio for the obstacle-free case.

A proportional contact representation of a planar graph is one where each vertex is represented by a simple polygon with area proportional to a given weight and adjacencies between polygons represent edges between the corresponding pairs of vertices. In this paper we study proportional contact representations that use only rectilinear polygons and contain no unused area or hole. There is an alg...

Let P and Q be two disjoint rectilinear polygons in the plane. We say P and Q are in Case 1 if there exists a rectilinear line segment to connect them; otherwise, we say they are in Case 2. In this paper, we present optimal algorithms for solving the following problem. Given two disjoint rectilinear polygons P and Q in the plane, we want to add a rectilinear line segment to connect them when th...

Fifteen years ago, an intriguing area was found in human visual cortex. This area (the parahippocampal place area [PPA]) was initially interpreted as responding selectively to images of places. However, subsequent studies reported that PPA also responds strongly to a much wider range of image categories, including inanimate objects, tools, spatial context, landmarks, objectively large objects, ...

Let S be a set of n points in R, and let r be a parameter with 1 6 r 6 n. A rectilinear r-partition for S is a collection Ψ(S) := {(S1, b1), . . . , (St, bt)}, such that the sets Si form a partition of S, each bi is the bounding box of Si, and n/2r 6 |Si| 6 2n/r for all 1 6 i 6 t. The (rectilinear) stabbing number of Ψ(S) is the maximum number of bounding boxes in Ψ(S) that are intersected by a...

Isochrones are generally defined as the set of all space points from which a query point can be reached in a given timespan, and they are used in urban planning to conduct reachability and coverage analyzes in a city. In a spatial network representing the street network, an isochrone is represented as a subgraph of the street network. Such a network representation is not always sufficient to de...

In this paper we give an optimal O(n log n) time and O(n) space algorithm to compute the rectilinear convex layers of a set S of n points on the plane. We also compute the rotation of S that minimizes the number of rectilinear convex layers in O(n log n) time and O(n) space.