Given an n-vertex and m-edge non-negatively real-weighted graph G = (V, E, w), whose vertices are partitioned into a set of k clusters, a clustered network design problem on G consists of finding a (possibly optimal) solution to a given network design problem on G, subject to some additional constraint on its clusters. In this paper, we focus on the classic shortest-path tree problem and summar...

This article discusses the addition of an energy parameter to the shortest path execution process; namely, the energy expenditure by a character during execution of the path. Given a simple environment in which a character has the ability to perform actions related to locomotion, such as walking and stair stepping, current techniques execute the shortest path based on the length of the extracte...

We present a method for creating geometric models of dendritic forms. Dendritic shapes are commonplace in the natural world; some examples of objects exhibiting dendritic shape include lichens, coral, trees, lightning, rivers, crystals, and venation patterns. Our method first generates a regular lattice with randomly weighted edges, then finds least-cost paths through the lattice. Multiple path...

we design a two-stage scheme to consider trajectory planning problem of two mobile manipulators for cooperative transportation of a rigid body in presence of static obstacles. within the first stage, regarding the static obstacles we develop a method that searches the workspace for the shortest possible path between start and goal configurations by constructing a graph on a portion of the confi...

We pose the following questions: Given two points within a closed area W C R2, each with a prescribed direction of motion in it, (i) what is the shortest path of bounded curvature that joints them and lies completely in W? (ii) what is the minimum number of cusps one needs to design a path in W? This kind of questions appear in various applications, such as robot motion planning. The proposed a...

With the development of industrialization rapidly, vehicles have become an important part of people’s life. However, transportation system is becoming more and more complicated. The core problem of the complicated transportation system is how to avoid hotspots. In this paper, we present a graph model based on a multi-dimension weighted graph for path planning with avoiding hotspots. Firstly, we...

We consider the problem of computing shortest paths subject to an additional resource constraint such as a hard limit on the (positive) height difference of the path. This is typically of interest in the context of bicycle route planning, or when energy consumption is to be limited. So far, the exact computation of such constrained shortest paths was not feasible on large networks; we show that...

A shortest path joining two specified endpoint configurations that is constrained to have mean curvature at most ς on every non-zero length sub-path is called a ς-geodesic. A seminal result in non-holonomic motion planning is that (in the absence of obstacles) a 1-geodesic consists of either (i) a (unit-radius) circular arc followed by a straight segment followed by another circular arc, or (ii...

All-pairs shortest paths (APSP) can eliminate the need to search in a graph, providing optimal moves very fast. A major challenge is storing pre-computed APSP data efficiently. Recently, compression has successfully been employed to scale the use of APSP data to roadmaps and gridmaps of realistic sizes. We develop new techniques that improve the compression power of state-of-the-art methods by ...

We consider a problem of motion planning under uncertainty. A robot can navigate freely in the plane and, using a built-in vision system, can determine distances and angles. Initially, the robot stands at a point close to a an edge of a polygonal obstacle (e. g. a wall of a huge building) and faces a corner at distance 1 from its position. The other wall which forms the corner is invisible from...