4 research outputs found
Parking functions, labeled trees and DCJ sorting scenarios
In genome rearrangement theory, one of the elusive questions raised in recent
years is the enumeration of rearrangement scenarios between two genomes. This
problem is related to the uniform generation of rearrangement scenarios, and
the derivation of tests of statistical significance of the properties of these
scenarios. Here we give an exact formula for the number of double-cut-and-join
(DCJ) rearrangement scenarios of co-tailed genomes. We also construct effective
bijections between the set of scenarios that sort a cycle and well studied
combinatorial objects such as parking functions and labeled trees.Comment: 12 pages, 3 figure
Efficient Sampling of Parsimonious Inversion Histories with Application to Genome Rearrangement in Yersinia
Inversions are among the most common mutations acting on the order and orientation of genes in a genome, and polynomial-time algorithms exist to obtain a minimal length series of inversions that transform one genome arrangement to another. However, the minimum length series of inversions (the optimal sorting path) is often not unique as many such optimal sorting paths exist. If we assume that all optimal sorting paths are equally likely, then statistical inference on genome arrangement history must account for all such sorting paths and not just a single estimate. No deterministic polynomial algorithm is known to count the number of optimal sorting paths nor sample from the uniform distribution of optimal sorting paths