 # An Amoeba-Based Computer Calculated Approximate Solutions to a Very Hard Math Problem

These single-celled organisms have a strange computing capacity that allows them to generate approximate solutions to a computationally complex problem known as the “traveling salesman problem.”
December 21, 2018, 7:36pm
Image: Royal Society Open Science

A team of Japanese researchers from Keio University in Tokyo have demonstrated that an amoeba is capable of generating approximate solutions to a remarkably difficult math problem known as the “traveling salesman problem.”

The traveling salesman problem goes like this: Given an arbitrary number of cities and the distances between them, what is the shortest route a salesman can take that visits each city and returns to the salesman’s city of origin. It is a classic problem in computer science and is used as a benchmark test for optimization algorithms.

The traveling salesman problem is considered “NP hard,” which means that the complexity of calculating a correct solution increases exponentially the more cities are added to the problem. For example, there are only three possible solutions if there are four cities, but there are 360 possible solutions if there are six cities. It continues to increase exponentially from there.

Despite the exponential increase in computational difficulty with each city added to the salesman’s itinerary, computer scientists have been able to calculate the optimal solution to this problem for thousands of cities since the early 90s and recent efforts have been able to calculate nearly optimal solutions for millions of cities.

Amoebas are single-celled organisms without anything remotely resembling a central nervous system, which makes them seem like less than suitable candidates for solving such a complex puzzle. Yet as these Japanese researchers demonstrated, a certain type of amoeba can be used to calculate nearly optimal solutions to the traveling salesman problem for up to eight cities. Even more remarkably, the amount of time it takes the amoeba to reach these nearly optimal solutions grows linearly, even though the number of possible solutions increases exponentially.

As detailed in a paper published this week in Royal Society Open Science, the amoeba used by the researchers is called Physarum polycephalum, which has been used as a biological computer in several other experiments. The reason this amoeba is considered especially useful in biological computing is because it can extend various regions of its body to find the most efficient way to a food source and hates light.