News on an NP problem from an Amoeba

fresh_42

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No, joke, I really dreamt somebody has solved the NP=P problem these days. Well, as I didn't dream of the proof, it probably won't matter that I don't remember the outcome. But I never had expected help from this side:

Abstract
Choosing a better move correctly and quickly is a fundamental skill of living organisms that corresponds to solving a computationally demanding problem. A unicellular plasmodium of Physarum polycephalum searches for a solution to the travelling salesman problem (TSP) by changing its shape to minimize the risk of being exposed to aversive light stimuli. In our previous studies, we reported the results on the eight-city TSP solution. In this study, we show that the time taken by plasmodium to find a reasonably high-quality TSP solution grows linearly as the problem size increases from four to eight. Interestingly, the quality of the solution does not degrade despite the explosive expansion of the search space. Formulating a computational model, we show that the linear-time solution can be achieved if the intrinsic dynamics could allocate intracellular resources to grow the plasmodium terminals with a constant rate, even while responding to the stimuli. These results may lead to the development of novel analogue computers enabling approximate solutions of complex optimization problems in linear time.
https://royalsocietypublishing.org/doi/10.1098/rsos.180396
 
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Ameoba to be or not ameoba to be
that is the question for NP=?=P
 

anorlunda

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My, how unexpected. Your dream antenna seems right on.
 

fresh_42

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The question really bothers me. I knew someone who lost a bet on it (solved until somewhat in the 90s) and had to pay for a balloon trip across the Alps. But what makes it so exciting is the question beyond: Are there intrinsic difficulties out there or are we just not smart enough? That some Amoebas beats us to it is a bit embarrassing.
 
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I think its more a problem of solving it via simulation methods. The difference between computationally finding a geodesic vs actually letting gravity do its thing.
 
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However I think your view is valid too in that we haven't yet found a means to compute it quickly yet since we know its done in nature.
 

anorlunda

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Weren't there earlier reports of the traveling salesmen solved by bees or ants? I recall that they left scent trails, shortest paths had the strongest scent, and later ants followed the strongest scent.
 

fresh_42

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Weren't there earlier reports of the traveling salesmen solved by bees or ants? I recall that they left scent trails, shortest paths had the strongest scent, and later ants followed the strongest scent.
I think I've read something similar. On the other hand, IIRC (it's really long ago) then NP problems are solvable in P if there is an oracle tape attached to the TM. The scents can probably be interpreted as such a tape.
 

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