The discussion centers on the NP=P problem and its implications, particularly through the lens of biological computation demonstrated by the unicellular organism Physarum polycephalum. This organism effectively solves the traveling salesman problem (TSP) by adapting its shape to optimize movement and minimize exposure to light stimuli. Research indicates that the time required for the plasmodium to find high-quality TSP solutions increases linearly with problem size, while maintaining solution quality despite the expanding search space. These findings suggest potential advancements in analogue computing for solving complex optimization problems efficiently.
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https://royalsocietypublishing.org/doi/10.1098/rsos.180396Abstract
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 traveling 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.
Good comparison.jedishrfu said:The difference between computationally finding a geodesic vs actually letting gravity do its thing.
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.anorlunda said: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.