Multi-robot Symmetric Rendezvous Search on the Line with an Unknown Initial Distance

arXiv.org Artificial Intelligence

In this paper, we study the symmetric rendezvous search problem on the line with n > 2 robots that are unaware of their locations and the initial distances between them. In the symmetric version of this problem, the robots execute the same strategy. The multi-robot symmetric rendezvous algorithm, MSR presented in this paper is an extension our symmetric rendezvous algorithm, SR presented in [23]. We study both the synchronous and asynchronous cases of the problem. The asynchronous version of MSR algorithm is called MASR algorithm. We consider that robots start executing MASR at different times. We perform the theoretical analysis of MSR and MASR, and show that their competitive ratios are $O(n^{0.67})$ and $O(n^{1.5})$, respectively. Finally, we confirm our theoretical results through simulations.


How to detect a pattern? Problem and solution.

@machinelearnbot

Fifth issue: some of the great metrics (distances between kth-neighbors) might not have a simple mathematical formula. But we can use Monte-Carlo simulations to address this issue: simulate a random process, compute the distribution of distances (with confidence intervals) based on thousands of simulations, and compare with distances computed on your data. If distance distribution computed on the data set matches results from simulations, we are good, it means our data is probably random. However, we would have to make sure that distance distribution uniquely characterizes a Poisson process, and that no non-random processes could yield the same distance distribution. This exercise is known as goodness-of-fit testing: you try to see if your data support a specific hypothesis of randomness.


Hey! You Can Find Pi With a Random Walk. Here's How

WIRED

The best thing about pi is finding it in places you don't expect--like, say, a random walk. What is a random walk? The simplest location to start with is at the origin so x 0 meters. Move one meter to the right. Repeat as often as you like.


Hug a tree while you still can: U.S. forests are disappearing

Mashable

The Amazon rainforest and Indonesia's peat swamps aren't the only places suffering from deforestation. On the mainland U.S., swaths of forests are steadily disappearing, too. The forests themselves are growing farther and farther apart, researchers say. A new study found that the average distance between forest patches increased by nearly 1,690 feet -- or about 14 percent -- between 1992 and 2001. SEE ALSO: Meet the architect behind China's smog-sucking'vertical forests' Think of each forest patch as a sanctuary or transit hub for migratory animals and other species.


Calculate How Fast Quicksilver Is Moving in *X-Men Apocalypse*

WIRED

Just how fast is the X-Men character Quicksilver, also known as Peter Maximoff (and son of Magneto)? This would be a popular topic of debate at the comic book bar--if a comic book bar existed. It such a bar does exist, I have to go. We can take a crack at answering this question, starting with a scene from the 2016 movie X-Men: Apocalypse. In it, Quicksilver arrives at Xavier's School for Gifted Youngsters (the X-Men mansion).