algorithms-optimization / Extremal Set Theory, Algorithms

Optimal Chain Density and Space-Time Tradeoffs for the TSP

The paper nearly settles the tradeoff between the size of a set system over $[n]$ and its number of full chains, an extremal question raised by Johnson, Leader and Russell as a counterpart to Sperner-type results, and linked by recent work to the space and time complexity of Bellman–Held–Karp dynamic programming for permutation problems.

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The paper nearly settles the tradeoff between the size of a set system over $[n]$ and its number of full chains, an extremal question raised by Johnson, Leader and Russell as a counterpart to Sperner-type results, and linked by recent work to the space and time complexity of Bellman–Held–Karp dynamic programming for permutation problems.

The authors describe the tradeoff as nearly settled rather than settled.

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