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Search Algorithms, Finding Nemo

Over $90 million was spent searching for Malaysia Airlines Flight 370. The International Group for Historic Aircraft Recovery spent $2.2 million looking for Amelia Earhart. Both these searches have one thing in common: the subjects of the searches were stationary.

But would these searches have been successful had the subjects of the searches been moving around? The movement of the searcher in a situation where two individuals are looking for each other is always assumed. The searcher must move in the search. It is also advised that the subject of the search be stationary. Parents tell their children in amusement parks that standing still is the best way to be found. Running around in a panic would lead to both parties running around in circles. Survivalists too agree that in the event of a plane crash, staying near the wreckage is the best chance for rescue. But is there any truth to this?

We approached this question by simulating the movement of individuals mathematically, essentially representing them as points on a Cartesian plane defined by discrete values. In other words, the points could only exist on integer-value coordinates. To this end, a simple Java program was created to record trials of the points moving around randomly. If the points coexisted at a coordinate, we took it to mean that the searcher had met the subject of the search, ending the trial. In the end, we concluded that trials with points that both moved ended earlier on average than trials with only a single point moving. In other words, the simple simulation suggested that stranded individuals shouldn’t sit still and wait for help.

As a result, science seems to suggest that after a plane crash in the woods, you should pack in-flight meals in your backpack and set out in one direction. But this is not altogether accurate, because the simulation we ran falls apart when dealing with infinite grids. With no boundaries, it may take an infinite amount of time for a search to be resolved, and the Earth is without doubt an infinite grid because there’s no edge of the world. It works in an amusement park but doesn’t work so well in the middle of the Gobi desert.

So the art of the search is a great example of why multiple disciplines are necessary to solve the simplest questions. Physicists can’t do their job without statisticians and historians cannot do much without geographers. By using mathematics, we exploited reason, but the truth was not revealed. And if there’s one thing to take away from this, it’s that you should never get lost in an unbounded spatial plane without having an infinite number of searchers looking for you.

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