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Community Bot
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Since you are asking about an algorithmic perspective, I wanted to point out that a closely related variation (with logarithmic potential instead of hard core potential) is the subject of one of Smale's "Mathematical Problems for the Next Century." In Problem 7, Smale asks if there is a polynomial time algorithm (in a particular model of computation over real numbersin a particular model of computation over real numbers) to place $N$ points on the sphere so that the total energy is $O(\log N)$ above the minimum energy.

Now, for specific finite values of $N$, Neil Sloane has a table of best known spherical codes with references: http://neilsloane.com/packings/

Since you are asking about an algorithmic perspective, I wanted to point out that a closely related variation (with logarithmic potential instead of hard core potential) is the subject of one of Smale's "Mathematical Problems for the Next Century." In Problem 7, Smale asks if there is a polynomial time algorithm (in a particular model of computation over real numbers) to place $N$ points on the sphere so that the total energy is $O(\log N)$ above the minimum energy.

Now, for specific finite values of $N$, Neil Sloane has a table of best known spherical codes with references: http://neilsloane.com/packings/

Since you are asking about an algorithmic perspective, I wanted to point out that a closely related variation (with logarithmic potential instead of hard core potential) is the subject of one of Smale's "Mathematical Problems for the Next Century." In Problem 7, Smale asks if there is a polynomial time algorithm (in a particular model of computation over real numbers) to place $N$ points on the sphere so that the total energy is $O(\log N)$ above the minimum energy.

Now, for specific finite values of $N$, Neil Sloane has a table of best known spherical codes with references: http://neilsloane.com/packings/

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Yoav Kallus
Yoav Kallus
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Since you are asking about an algorithmic perspective, I wanted to point out that a closely related variation (with logarithmic potential instead of hard core potential) is the subject of one of Smale's "Mathematical Problems for the Next Century." In Problem 7, Smale asks if there is a polynomial time algorithm (in a particular model of computation over real numbers) to place $N$ points on the sphere so that the total energy is $O(\log N)$ above the minimum energy.

Now, for specific finite values of $N$, Neil Sloane has a table of best known spherical codes with references: http://neilsloane.com/packings/

Since you are asking about an algorithmic perspective, I wanted to point out that a closely related variation (with logarithmic potential instead of hard core potential) is the subject of one of Smale's "Mathematical Problems for the Next Century." In Problem 7, Smale asks if there is a polynomial time algorithm (in a particular model of computation over real numbers) to place $N$ points on the sphere so that the total energy is $O(\log N)$ above the minimum energy.

Since you are asking about an algorithmic perspective, I wanted to point out that a closely related variation (with logarithmic potential instead of hard core potential) is the subject of one of Smale's "Mathematical Problems for the Next Century." In Problem 7, Smale asks if there is a polynomial time algorithm (in a particular model of computation over real numbers) to place $N$ points on the sphere so that the total energy is $O(\log N)$ above the minimum energy.

Now, for specific finite values of $N$, Neil Sloane has a table of best known spherical codes with references: http://neilsloane.com/packings/

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Yoav Kallus
Yoav Kallus
  • 6k
  • 3
  • 41
  • 57

Since you are asking about an algorithmic perspective, I wanted to point out that a closely related variation (with logarithmic potential instead of hard core potential) is the subject of one of Smale's "Mathematical Problems for the Next Century." In Problem 7, Smale asks if there is a polynomial time algorithm (in a particular model of computation over real numbers) to place $N$ points on the sphere so that the total energy is $O(\log N)$ above the minimum energy.