Since ancient Greece, researchers have tried to isolate special rational points on curves. Now they have the first ever formula that applies uniformly to all curves ...

Autonomous vehicles have made remarkable progress over the past decade, accumulating millions of miles and performing well on highways, in controlled test areas, and in select urban zones. However, ...

A recent breakthrough of Bernstein, Nanongkai, and Wulff-Nilsen established the first near-linear time algorithm for negative-weight single-source shortest paths on integer-weighted graphs. We refine ...

Shortest path algorithms sit at the heart of modern graph theory and many of the systems that move people, data, and goods around the world. After nearly seventy years of relying on the same classic ...

Abstract: Multiobjective shortest path problem (MSPP) is one of the most critical issues in network optimization, aimed at identifying all efficient paths across conflicting objectives. Nowadays, ...

There is a new sorting algorithm a deterministic O(m log2/3 n)-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition ...

Abstract: Multi-objective multi-point shortest path planning problems are commonly encountered in real-world applications. Numerous path planning algorithms have been proposed to accommodate different ...

In a contest of little quality, it was Niclas Fullkrug who served a reminder of what he offers to West Ham United’s attack when fully fit. The encounter against Wolverhampton Wanderers had little ...

Finding the shortest path in a network is a classical problem, and a variety of search strategies have been proposed to solve it. In this paper, we review traditional approaches for finding shortest ...

Dijkstra’s algorithm is great as long as we have no negative weight edges in our graph. But there are many problems for which it is natural to represent weights with positive and negative values—gains ...

The original version of this story appeared in Quanta Magazine. If you’ve been making the same commute for a long time, you’ve probably settled on what seems like the best route. But “best” is a ...