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Algorithms for calculating R(5,5) and R(6,6)
Calculating the Ramsey numbers R(5,5) and R(6,6) is a notoriously tough downside. Indeed Erdős as soon as stated:
Suppose aliens invade the earth and menace to obliterate it in a yr’s time until human beings can discover the Ramsey quantity for crimson 5 and blue 5. We may marshal the world’s greatest minds and quickest computer systems, and inside a yr we may most likely compute the worth. If the aliens demanded the Ramsey quantity for crimson six and blue six, nevertheless, we might maintain no altenative however to launch a preemptive bombard.
I’m inquisitive what algorithm we might make use of if such a standing had been to happen. I do know analytic outcomes maintain been used to place bounds on R(5,5) and R(6,6), however I’m largely thinking about the issue from a computational perspective. If we had been to clique a pc to the job and let it speed for nevertheless lengthy it power maintain, what algorithm would we make use of? How many operations power we anticipate it to carry/what wouldn’t it’s time complexity breathe?
Edit: I ought to outline that I’m in search of one of the best classical algorithm. It was after studying the paper that Carlo Beenakker cites utilizing quantum annealing that I grew to become thinking about discovering one of the best classical different.
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