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A classical problem in comparative genomics is to compute the rearrangement distance, that is the minimum number of large-scale rearrangements required to transform a given genome into another given genome. While the most traditional approaches in this area are family-based, i.e., require the classification of DNA fragments into families, more recently an alternative family-free approach was proposed, and consists of studying the rearrangement distances without prior family assignment. On the one hand the computation of genomic distances in the family-free setting helps to match occurrences of duplicated genes and find homologies, but on the other hand this computation is NP-hard. In this paper, by letting structural rearrangements be represented by the generic double cut and join (DCJ) operation and also allowing insertions and deletions of DNA segments, we propose a new and more general family-free genomic distance, providing an efficient ILP formulation to solve it. Our experiments show that the ILP produces accurate results and can handle not only bacterial genomes, but also fungi and insects, or subsets of chromosomes of mammals and plants.
The computation of genomic distances has been a very active field of computational comparative genomics over the last 25 years. Substantial results include the polynomial-time computability of the inversion distance by Hannenhalli and Pevzner in 1995
In the literature on parameterized graph problems, there has been an increased effort in recent years aimed at exploring novel notions of graph edit-distance that are more powerful than the size of a modulator to a specific graph class. In this line
A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and preprocessing t
In this paper, we first define the pre-Lie family algebra associated to a dendriform family algebra in the case of a commutative semigroup. Then we construct a pre-Lie family algebra via typed decorated rooted trees, and we prove the freeness of this
Approximating the length of the longest increasing sequence (LIS) of an array is a well-studied problem. We study this problem in the data stream model, where the algorithm is allowed to make a single left-to-right pass through the array and the key