Information distance can be defined not only between two strings but also in a finite multiset of strings of cardinality greater than two. We determine a best upper bound on the information distance. It is exact, since the upper bound on the information distance for all multisets is the same as the lower bound for infinitely many multisets of each of infinitely many cardinalities, up to a constant additive term.

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IEEE Transactions on Information Theory
Algorithms and Complexity

Vitányi, P.M.B. (2017). Exact expression for information distance. IEEE Transactions on Information Theory, 63(8), 4725–4728. doi:10.1109/TIT.2017.2686883