The dot clouds, one red and one blue, resemble a cell nearly done splitting. Each cloud represents a group of social media users so polarized that the threads connecting them are tenuous at best. Democrat and Republican, left and right, pro and con.

Bridging the divide between these echo chambers has kept Kiran Garimella, a computer science PhD researcher at Aalto University, up at night.

"It's a hard task for sure," he told me — a huge understatement. "I've had a lot of sleepless nights." He and his international colleagues from Aalto University in Helsinki recently developed an algorithm that could help Twitter users on either side of a divisive issue step out of their respective bubbles and reach across the aisle.

Personalized recommendations on sites like Facebook and Twitter mean that when we search for information, we tend to be presented with suggestions that already conform to our beliefs. This "Truman Show"-like reinforcement creates what social scientists call "bubble filters" that shut out opposing viewpoints, Garimella explained.

The computer scientists started with large data sets from well-known Twitter users with numerous followers, analyzed the connections among them, and looked at how the users interact. Once the researchers had quantified the users' bubbles, called retweet networks, they parsed the data for keywords and hashtags.

Then their method made suggestions for content most likely to be shared by members of both sides based on factors such as how biased the Twitter users already are and the content's popularity.

Garimella developed the algorithm with associate professor Aristides Gionis, and postdocs Michael Mathioudakis and Gianmarco De Francisci Morales. Their paper describing the approach recently won an award at the ACM International Conference on Web Search and Data Mining.

RELATED: New Tool Shows You Twitter Feeds of Users With Opposite Political Views

Garimella's interest in political polarization sparked in 2012, when he was based in Barcelona working as a research engineer for Yahoo. His team was tasked with looking at political coverage of the U.S. presidential election and understanding how people search the web for political news. His PhD became a natural continuation of that, he said. At Aalto University, he studied online news consumption, which led to a closer look at how news gets shared.

His group's tool has several advantages over other approaches to connect opposing viewpoints, Garimella told me. For one, it works automatically on a large scale and can be applied to thousands of people. In addition, the tool isn't dependent on any particular language or domain. They tested the tool on data sets from Russian Twitter users and Indian Twitter users split over controversial national issues.

In an ideal scenario, the tool would become a recommendation widget for Twitter, Garimella said. After showing how biased you are on a scale, the self-help tool could make suggestions on what to retweet to become less biased.

In research currently undergoing peer review, the Aalto University team tested the suggestions pulled from their algorithm on a few hundred Twitter users. Around 60 percent indicated those recommendations made sense, which is a favorable result, according to Garimella.

"We don't really connect the extremes, but try to find the middle ground," he said.

WATCH VIDEO: How Powerful Is Twitter?