4,733 research outputs found
An asymmetric approach to preserve common intervals while sorting by reversals
Dias Vieira Braga M, Gautier C, Sagot M-F. An asymmetric approach to preserve common intervals while sorting by reversals. Algorithms for Molecular Biology. 2009;4(1):16.Background: The reversal distance and optimal sequences of reversals to transform a genome into another are useful tools to analyse evolutionary scenarios. However, the number of sequences is huge and some additional criteria should be used to obtain a more accurate analysis. One strategy is searching for sequences that respect constraints, such as the common intervals (clusters of co-localised genes). Another approach is to explore the whole space of sorting sequences, eventually grouping them into classes of equivalence. Recently both strategies started to be put together, to restrain the space to the sequences that respect constraints. In particular an algorithm has been proposed to list classes whose sorting sequences do not break the common intervals detected between the two inital genomes A and B. This approach may reduce the space of sequences and is symmetric (the result of the analysis sorting A into B can be obtained from the analysis sorting B into A). Results: We propose an alternative approach to restrain the space of sorting sequences, using progressive instead of initial detection of common intervals (the list of common intervals is updated after applying each reversal). This may reduce the space of sequences even more, but is shown to be asymmetric. Conclusions: We suggest that our method may be more realistic when the relation ancestor-descendant between the analysed genomes is clear and we apply it to do a better characterisation of the evolutionary scenario of the bacterium Rickettsia felis with respect to one of its ancestors
Average-case analysis of perfect sorting by reversals (Journal Version)
Perfect sorting by reversals, a problem originating in computational
genomics, is the process of sorting a signed permutation to either the identity
or to the reversed identity permutation, by a sequence of reversals that do not
break any common interval. B\'erard et al. (2007) make use of strong interval
trees to describe an algorithm for sorting signed permutations by reversals.
Combinatorial properties of this family of trees are essential to the algorithm
analysis. Here, we use the expected value of certain tree parameters to prove
that the average run-time of the algorithm is at worst, polynomial, and
additionally, for sufficiently long permutations, the sorting algorithm runs in
polynomial time with probability one. Furthermore, our analysis of the subclass
of commuting scenarios yields precise results on the average length of a
reversal, and the average number of reversals.Comment: A preliminary version of this work appeared in the proceedings of
Combinatorial Pattern Matching (CPM) 2009. See arXiv:0901.2847; Discrete
Mathematics, Algorithms and Applications, vol. 3(3), 201
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
Polynomial-time sortable stacks of burnt pancakes
Pancake flipping, a famous open problem in computer science, can be
formalised as the problem of sorting a permutation of positive integers using
as few prefix reversals as possible. In that context, a prefix reversal of
length k reverses the order of the first k elements of the permutation. The
burnt variant of pancake flipping involves permutations of signed integers, and
reversals in that case not only reverse the order of elements but also invert
their signs. Although three decades have now passed since the first works on
these problems, neither their computational complexity nor the maximal number
of prefix reversals needed to sort a permutation is yet known. In this work, we
prove a new lower bound for sorting burnt pancakes, and show that an important
class of permutations, known as "simple permutations", can be optimally sorted
in polynomial time.Comment: Accepted pending minor revisio
A survey on algorithmic aspects of modular decomposition
The modular decomposition is a technique that applies but is not restricted
to graphs. The notion of module naturally appears in the proofs of many graph
theoretical theorems. Computing the modular decomposition tree is an important
preprocessing step to solve a large number of combinatorial optimization
problems. Since the first polynomial time algorithm in the early 70's, the
algorithmic of the modular decomposition has known an important development.
This paper survey the ideas and techniques that arose from this line of
research
On the effective and automatic enumeration of polynomial permutation classes
We describe an algorithm, implemented in Python, which can enumerate any
permutation class with polynomial enumeration from a structural description of
the class. In particular, this allows us to find formulas for the number of
permutations of length n which can be obtained by a finite number of block
sorting operations (e.g., reversals, block transpositions, cut-and-paste
moves)
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