EDoP Distance Between Sets of Incomplete Permutations: Application to Bacteria Classification Based on Gene Order

In this work, we extend measures of distance between permutations to support incomplete permutations. Modeling and comparing incomplete permutations are a challenging computational problem of practical importance in many applications in bioinformatics and social science. We show that the proposed distance measure admits a closed-form expression and can be efficiently computed on sets of permutations involving several missing elements. We demonstrate the proposed method on the classification of bacteria from different phyla based on gene order.