Carla Negri Lintzmayer

Sorting Permutations by Prefix and Suffix Versions of Reversals and Transpositions

Reversals and transpositions are the most common kinds of genome rearrangements, which allow us to establish the divergence between individuals along evolution. When the rearrangements affect segments from the beginning or from the end of the genome, we say they are prefix or suffix rearrangements, respectively. This paper presents the first approximation algorithms for the problems of Sorting by Prefix Reversals and Suffix Reversals, Sorting by Prefix Transpositions and Suffix Transpositions and Sorting by Prefix Reversals, Prefix Transpositions, Suffix Reversals and Suffix Transpositions, all of them with factor 2. We also present the intermediary algorithms that lead us to the main results.

A general heuristic for genome rearrangement problems.

In this paper, we present a general heuristic for several problems in the genome rearrangement field. Our heuristic does not solve any problem directly, it is rather used to improve the solutions provided by any non-optimal algorithm that solve them. Therefore, we have implemented several algorithms described in the literature and several algorithms developed by ourselves. As a whole, we implemented 23 algorithms for 9 well known problems in the genome rearrangement field. A total of 13 algorithms were implemented for problems that use the notions of prefix and suffix operations. In addition, we worked on 5 algorithms for the classic problem of sorting by transposition and we conclude the experiments by presenting results for 3 approximation algorithms for the sorting by reversals and transpositions problem and 2 approximation algorithms for the sorting by reversals problem. Another algorithm with better approximation ratio can be found for the last genome rearrangement problem, but it is purely theoretical with no practical implementation. The algorithms we implemented in addition to our heuristic lead to the best practical results in each case. In particular, we were able to improve results on the sorting by transpositions problem, which is a very special case because many efforts have been made to generate algorithms with good results in practice and some of these algorithms provide results that equal the optimum solutions in many cases. Our source codes and benchmarks are freely available upon request from the authors so that it will be easier to compare new approaches against our results.

On Sorting of Signed Permutations by Prefix and Suffix Reversals and Transpositions

A reversal inverts a segment and the signs of the elements of this segment in a permutation. A transposition exchanges the position of two consecutive segments. These are the most common kinds of genome rearrangements. In this paper, we introduce the study of prefix and suffix versions of these operations, that is, when only segments of the beginning or of the end are involved, when considering signed permutations. We gave asymptotic approximation algorithms of factor two for three new problems: when prefix and suffix reversals are allowed, when prefix reversals and prefix transpositions are allowed, and when prefix and suffix reversals and prefix and suffix transpositions are allowed.

Register Allocation with Graph Coloring by Ant Colony Optimization

The goal of register allocation is to allocate an unbounded number of program values to a finite number of machine registers. In this paper, we describe a new algorithm for intraprocedural register allocation called CA-RT-RA, an algorithm that extends a classic graph coloring register allocator to use our graph coloring algorithm Color Ant-RT. The experiments demonstrated that our algorithm is able to minimize the amount of spills, thereby improving the quality of the generated code. CA-RT-RA is interesting in applications where compile time is not a concern, but the code quality.

On the Diameter of Rearrangement Problems

When we consider the Genome Rearrangements area, the problems of finding the distance of a permutation and finding the diameter of all permutations of the same size are the most common studied. In this paper, we considered problems for which no known results were presented regarding their diameters. We present some families of permutations whose distance is identical to the diameter for small sizes. They allowed us to gave bounds for the diameters of the problems we considered, as well as conjectures regarding the exact value.

Toward Better Performance of ColorAnt ACO Algorithm

This paper presents the Color Ant-RT algorithm version 3, an algorithm for graph coloring problems which is based on the Ant Colony Optimization metaheuristic and uses Tabu Search as local search. The experiments demonstrated that ColorAnt3-RT is a promising option in finding good approximations to the best known results for geometric random, geometric standard and le450 graphs of DIMACS benchmark in an acceptable runtime, also, it is good in minimizing the amount of conflicts, the main problem of graph coloring with a fixed number of colors.

Sorting permutations by prefix and suffix rearrangements

Some interesting combinatorial problems have been motivated by genome rearrangements, which are mutations that affect large portions of a genome. When we represent genomes as permutations, the goal is to transform a given permutation into the identity permutation with the minimum number of rearrangements. When they affect segments from the beginning (respectively end) of the permutation, they are called prefix (respectively suffix) rearrangements. This paper presents results for rearrangement problems that involve prefix and suffix versions of reversals and transpositions considering unsigned and signed permutations. We give 2-approximation and ([Formula: see text])-approximation algorithms for these problems, where [Formula: see text] is a constant divided by the number of breakpoints (pairs of consecutive elements that should not be consecutive in the identity permutation) in the input permutation. We also give bounds for the diameters concerning these problems and provide ways of improving the practical results of our algorithms.

Approximation algorithms for sorting by length-weighted prefix and suffix operations

We addressed sorting permutations by prefix and suffix reversals and transpositions.We initiated the study of these rearrangements in a length-weighted context.We presented approximation algorithms for 10 such problems. The traditional approach for the problems of sorting permutations by rearrangements is to consider that all operations have the same unitary cost. In this case, the goal is to find the minimum number of allowed rearrangements that are needed to sort a given permutation, and numerous efforts have been made over the past years regarding these problems. On the other hand, a long rearrangement (which is in fact a mutation) is more likely to disturb the organism. Therefore, weights based on the length of the segment involved may have an important role in the evolutionary process. In this paper we present the first results regarding problems of sorting permutations by length-weighted operations that consider rearrangement models with prefix and suffix variations of reversals and transpositions, which are the two most common types of genome rearrangements. Our main results are O ( lg 2 ? n ) -approximation algorithms for 10 such problems.

Register Allocation by Evolutionary Algorithm

Graph coloring is a highly effective approach to intraprocedural register allocation. In this paper, we describe a new algorithm for intraprocedural register allocation called HECRA, an algorithm that extends a classic graph coloring register allocator to use a hybrid evolutionary coloring algorithm. The experiments demonstrated that our algorithm is able to minimize the amount of spills, thereby improving the quality of the generated code. Besides, HECRA is interesting in contexts where compile time is a concern, and not only the quality of the generated code.

Sorting Permutations by Limited-Size Operations.

Estimating the evolutionary distance between genomes of two organisms is a challenging task for Computational Biology. One of the most well-accepted ways to do this is to consider the size of the smallest sequence of rearrangement events required to transform one genome into another, characterizing the rearrangement distance problem. Computationally, genomes can be represented as permutations of integers and, with this, the problem can be reduced to transforming a permutation into the identity with the minimum number of operations (sorting the permutation). These operations are given by a rearrangement model and they affect segments of a genome in different ways. Among the most common models are those that allow only reversals, only transpositions, or both of them. In this paper we study sorting permutations when a restriction of biological relevance is added: the size of the rearrangements should be at most a given value \(\lambda \). Some results are known for \(\lambda = 2\) and \(\lambda = 3\) but, to the best of our knowledge, there are no results for \(\lambda > 3\). We consider rearrangement models that allow reversals and/or transpositions for sorting unsigned permutations given any value of \(\lambda \). We present approximation algorithms for 3 such problems, where the approximation factors depend on \(\lambda \) and/or on the size of the permutations.