arXiv subjects

Irena Rusu

Publications and source records attributed to Irena Rusu.

21 records · Page 2Linked to original sources

arXiv2011

Pancake Flipping is Hard

Pancake Flipping is the problem of sorting a stack of pancakes of different sizes (that is, a permutation), when the only allowed operation is to insert a spatula anywhere in the stack and to flip the pancakes above it (that is, to perform a prefix reversal). In the burnt variant, one side of each pancake is marked as burnt, and it is required to finish with all pancakes having the burnt side down. Computing the optimal scenario for any stack of pancakes and determining the worst-case stack for any stack size have been challenges over more than three decades. Beyond being an intriguing combinatorial problem in itself, it also yields applications, e.g. in parallel computing and computational biology. In this paper, we show that the Pancake Flipping problem, in its original (unburnt) variant, is NP-hard, thus answering the long-standing question of its computational complexity.

cs.CC↗

arXiv2010

Sorting by Transpositions is Difficult

In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, is, according to numerous studies, a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations, called the Sorting by Transpositions problem, has been introduced by Bafna and Pevzner in 1995. It has naturally been the focus of a number of studies, but the computational complexity of this problem has remained undetermined for 15 years. In this paper, we answer this long-standing open question by proving that the Sorting by Transpositions problem is NP-hard. As a corollary of our result, we also prove that the following problem is NP-hard: given a permutation pi, is it possible to sort pi using db(pi)/3 permutations, where db(pi) is the number of breakpoints of pi?

cs.DS↗

arXiv2008

On the Approximability of Comparing Genomes with Duplicates

A central problem in comparative genomics consists in computing a (dis-)similarity measure between two genomes, e.g. in order to construct a phylogeny. All the existing measures are defined on genomes without duplicates. However, we know that genes can be duplicated within the same genome. One possible approach to overcome this difficulty is to establish a one-to-one correspondence (i.e. a matching) between genes of both genomes, where the correspondence is chosen in order to optimize the studied measure. In this paper, we are interested in three measures (number of breakpoints, number of common intervals and number of conserved intervals) and three models of matching (exemplar, intermediate and maximum matching models). We prove that, for each model and each measure M, computing a matching between two genomes that optimizes M is APX-hard. We also study the complexity of the following problem: is there an exemplarization (resp. an intermediate/maximum matching) that induces no breakpoint? We prove the problem to be NP-Complete in the exemplar model for a new class of instances, and we show that the problem is in P in the maximum matching model. We also focus on a fourth measure: the number of adjacencies, for which we give several approximation algorithms in the maximum matching model, in the case where genomes contain the same number of duplications of each gene.

q-bio.QM↗