Related papers: Sorting With Forbidden Intermediates
The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problem's hardness. We study the quantum…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
The allowed patterns of a map on a one-dimensional interval are those permutations that are realized by the relative order of the elements in its orbits. The set of allowed patterns is completely determined by the minimal patterns that are…
The use of permutation polynomials has appeared, along to their compositional inverses, as a good choice in the implementation of cryptographic systems. Hence, there has been a demand for constructions of these polynomials which…
In the evolution of a genome, the gene sequence is sometimes rearranged, for example by transposition of two adjacent gene blocks. In biocombinatorics, one tries to reconstruct these rearrangement incidents from the resulting permutation.…
Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place,…
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…
Predictive algorithms are now used to help distribute a large share of our society's resources and sanctions, such as healthcare, loans, criminal detentions, and tax audits. Under the right circumstances, these algorithms can improve the…
Constraint problems can be trivially solved in parallel by exploring different branches of the search tree concurrently. Previous approaches have focused on implementing this functionality in the solver, more or less transparently to the…
Following the footprints of what have been done with the algorithm Stacksort, we investigate the preimages of the map associated with a slightly less well known algorithm, called Queuesort. After having described an equivalent version of…
We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…
The (strong) Bruhat order for permutations provides a partial ordering defined as follows: two permutations are comparable if one can be obtained from the other by a sequence of adjacent transpositions that each increase the number of…
Many important applications in biochemistry, materials science, and catalysis sit squarely at the interface between quantum and statistical mechanics: coherent evolution is interrupted by discrete events, such as binding of a substrate or…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
We investigate how sorting algorithms efficiently overcome the exponential size of the permutation space. Our main contribution is a new continuous-time formulation of sorting as a gradient flow on the permutohedron, yielding an independent…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
We introduce a novel framework of graph modifications specific to interval graphs. We study interdiction problems with respect to these graph modifications. Given a list of original intervals, each interval has a replacement interval such…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…