Determining the least expensive path for a new subway line underneath a metropolis like New York City is a colossal planning challenge—involving thousands of potential routes through hundreds of city ...

For non-planar graphs, such solutions are computationally intractable," explained the researchers. The algorithm relies on the Kac-Ward formalism, a mathematical method that allows exact computation ...

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 ...

Companies are increasingly using pricing algorithms and other AI systems to develop and improve their ability to promptly respond to market conditions, innovate product offerings, and set prices.