Related papers: Sorting by Prefix Block-Interchanges
The genome rearrangement problem computes the minimum number of operations that are required to sort all elements of a permutation. A block-interchange operation exchanges two blocks of a permutation which are not necessarily adjacent and…
In this work, we consider a restricted case of the well studied Sorting by Block Interchanges problem. We put an upper bound k on the length of the blocks (substrings) to be interchanged at each step. We call the problem Sorting by k-Block…
We prove a lower and an upper bound on the number of block moves necessary to sort a permutation. We put our results in contrast with existing results on sorting by block transpositions, and raise some open questions.
We use an interesting result of probabilistic flavor concerning the product of two permutations consisting of one cycle each to find an explicit formula for the average number of block interchanges needed to sort a permutation of length…
In the context of the genome rearrangement problem, we analyze two well known models, namely the block transposition and the prefix block transposition models, by exploiting the connection with the notion of permutation pattern. More…
In this paper we present a simple framework to study various distance problems of permutations, including the transposition and block-interchange distance of permutations as well as the reversal distance of signed permutations. These…
In this paper we study several variations of the \emph{pancake flipping problem}, which is also well known as the problem of \emph{sorting by prefix reversals}. We consider the variations in the sorting process by adding with prefix…
We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…
A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are…
A Genome rearrangement problem studies large-scale mutations on a set of DNAs in living organisms. Various rearrangements like reversals, transpositions, translocations, fissions, fusions, and combinations and different variations have been…
We consider the problem of upper bounding the number of circular transpositions needed to sort a permutation. It is well known that any permutation can be sorted using at most $n(n-1)/2$ adjacent transpositions. We show that, if we allow…
The prefix exchange distance of a permutation is the minimum number of exchanges involving the leftmost element that sorts the permutation. We give new combinatorial proofs of known results on the distribution of the prefix exchange…
We address the problem of finding the minimal number of block interchanges (exchange of two intervals) required to transform a duplicated linear genome into a tandem duplicated linear genome. We provide a formula for the distance as well as…
A number of fields, including the study of genome rearrangements and the design of interconnection networks, deal with the connected problems of sorting permutations in "as few moves as possible", using a given set of allowed operations, or…
The study of sorting permutations by block interchanges has recently been stimulated by a phenomenon observed in the genome maintenance of certain ciliate species. The result was the identification of a block interchange operation that…
We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations…
The task of learning to map an input set onto a permuted sequence of its elements is challenging for neural networks. Set-to-sequence problems occur in natural language processing, computer vision and structure prediction, where…
We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a…
We introduce a new sorting device for permutations which makes use of a pop stack augmented with a bypass operation. This results in a sorting machine, which is more powerful than the usual Popstacksort algorithm and seems to have never…
We study sorting of permutations by random swaps if each comparison gives the wrong result with some fixed probability $p<1/2$. We use this process as prototype for the behaviour of randomized, comparison-based optimization heuristics in…