Is a straight line the shortest path?

The shortest path is not always a straight line

In this paper, we leverage the concept of the metric backbone to improve the efficiency of large-scale graph analytics. The metric backbone is the minimum subgraph that preserves the shortest paths of a weighted graph. We use the metric backbone in place of the original graph to compute various graph metrics exactly or with good approximation. By computing on a smaller graph, we improve the per...

Velocity Planning for a Robot Moving along the Shortest Straight Line Path Among Moving Obstacles

Approximating the shortest path in line arrangements

Suppose one has a line arrangement and one wants to find a shortest path from one point lying on a line of the arrangement to another such point. The best known time bound for computing this is O(n2). We develop an algorithm that finds a 1 + approximation of the shortest path in time O(n logn+ (minfn; 1 2 g)1 log 1 ).

When the path is never shortest: a reality check on shortest path biocomputation

Shortest path problems are a touchstone for evaluating the computing performance and functional range of novel computing substrates. Much has been published in recent years regarding the use of biocomputers to solve minimal path problems such as route optimisation and labyrinth navigation, but their outputs are typically difficult to reproduce and somewhat abstract in nature, suggesting that bo...

A Shortest Path Approach for Vibrating Line Detection and Tracking

This paper describes an approach based on the shortest path method for the detection and tracking of vibrating lines. The detection and tracking of vibrating structures, such as lines and cables, is of great importance in areas such as civil engineering, but the specificities of these scenarios make it a hard problem to tackle. We propose a twostep approach consisting of line detection and subs...