On a Subset Metric

For a bounded metric space X, we define a metric on the set of all finite subsets of X. This generalizes the sequence-subset distance introduced by Wentu Song, Kui Cai and Kees A. Schouhamer Immink to study error correcting codes for DNA based data storage. This work also complements the work of Eiter and Mannila where they study extensions of distance functions to subsets of a space in the context of various applications.