An algorithm is presented for computing geodesic furthest neighbors for all the vertices of a simple polygon, where geodesic denotes the fact that distance between two points of the polygon is defined as the length of an Euclidean shortest path connecting them within the polygon. The algorithm runs in O(n log n) time and uses O(n) space; n being the number of vertices of the polygon. As a corol...

We present an algorithm to find an Euclidean Shortest Path from a source vertex s to a sink vertex t in the presence of obstacles in R. Our algorithm takes O(T +m(lgm)(lg n)) time and O(n) space. Here, O(T ) is the time to triangulate the polygonal region, m is the number of obstacles, and n is the number of vertices. This bound is close to the known lower bound of O(n+m lgm) time and O(n) spac...

Chazelle’s triangulation [1] forms today the common basis for linear-time Euclidean shortest path (ESP) calculations (where start and end point are given within a simple polygon). This paper provides an alternative method for subdividing a simple polygon into “basic shapes”, using trapezoids instead of triangles. The authors consider the presented method as being substantially simpler than the ...

We study the problem of interdicting the arcs in a network in order to maximize the shortest s–t path length. “Interdiction” is an attack on an arc that destroys the arc or increases its effective length; there is a limited interdiction budget. We formulate this bilevel, max–min problem as a mixed-integer program (MIP), which can be solved directly, but we develop more efficient decomposition a...

The shortest path problem in the time dependent network is an important extension of the classical shortest path problem and has been widely applied in real life. It is known as nonlinear and NP-hard. Therefore, the algorithms of the classical shortest path are incapable to solve this problem. In this paper, the models of the shortest path problem in the time dependent network are formulated an...

This paper considers the shortest path problem with fuzzy arc lengths. According to different decision criteria, the concepts of expected shortest path, a-shortest path and the most shortest path in fuzzy environment are originally proposed, and three types of models are formulated. In order to solve these models, a hybrid intelligent algorithm integrating simulation and genetic algorithm is pr...