Related papers: Lower bounding edit distances between permutations
We study the reconfiguration of odd matchings of combinatorial graphs. Odd matchings are matchings that cover all but one vertex of a graph. A reconfiguration step, or flip, is an operation that matches the isolated vertex and,…
Evolutionary algorithms solve problems by simulating the evolution of a population of candidate solutions. We focus on evolving permutations for ordering problems like the traveling salesperson problem (TSP), as well as assignment problems…
The problem of reconstructing strings from substring information has found many applications due to its importance in genomic data sequencing and DNA- and polymer-based data storage. One practically important and challenging paradigm…
Understanding the dynamics of genome rearrangements is a major issue of phylogenetics. Phylogenetics is the study of species evolution. A major goal of the field is to establish evolutionary relationships within groups of species, in order…
For a fixed graph class $\Pi$, the goal of $\Pi$-Modification is to transform an input graph $G$ into a graph $H\in\Pi$ using at most $k$ modifications. Vertex and edge deletions are common operations, and their (parameterized) complexity…
Hyperbolicity is a graph parameter which indicates how much the shortest-path distance metric of a graph deviates from a tree metric. It is used in various fields such as networking, security, and bioinformatics for the classification of…
This paper introduces a new way to define a genome rearrangement distance, using the concept of mean first passage time from probability theory. Crucially, this distance estimate provides a genuine metric on genome space. We develop the…
Two genomes over the same set of gene families form a canonical pair when each of them has exactly one gene from each family. Different distances of canonical genomes can be derived from a structure called breakpoint graph, which represents…
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…
When iteratively solving linear systems By=b with Hermitian positive semi-definite $B$, and in particular when solving least-squares problems for $Ax=b$ by reformulating them as $AA^\ast y=b$, it is often observed that SOR-type methods…
Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of $n$…
The classical rearrangement inequality provides bounds for the sum of products of two sequences under permutations of terms and show that similarly ordered sequences provide the largest value whereas opposite ordered sequences provide the…
Recently, a number of variants of the notion of cut-preserving hypergraph sparsification have been studied in the literature. These variants include directed hypergraph sparsification, submodular hypergraph sparsification, general notions…
The set of all error-correcting codes C over a fixed finite alphabet F of cardinality q determines the set of code points in the unit square with coordinates (R(C), delta (C)):= (relative transmission rate, relative minimal distance). The…
In this paper, we explore the theory and expand upon the practice of fitness landscape analysis for optimization problems over the space of permutations. Many of the computational and analytical tools for fitness landscape analysis, such as…
We study the problem of list ranking in the parallel external memory (PEM) model. We observe an interesting dual nature for the hardness of the problem due to limited information exchange among the processors about the structure of the…
Let $S_{\rm div}(n)$ denote the set of permutations $\pi$ of $n$ such that for each $1\leq j \leq n$ either $j \mid \pi(j)$ or $\pi(j) \mid j$. These permutations can also be viewed as vertex-disjoint directed cycle covers of the divisor…
Graph rewriting is a popular tool for the optimisation and modification of graph expressions in domains such as compilers, machine learning and quantum computing. The underlying data structures are often port graphs - graphs with labels at…
Phylogenetic networks are rooted directed acyclic graphs that represent evolutionary relationships between species whose past includes reticulation events such as hybridisation and horizontal gene transfer. To search the space of…
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of…