Related papers: Sorting With Forbidden Intermediates
In this paper, we present novel algorithms that efficiently compute a shortest reconfiguration sequence between two given dominating sets in trees and interval graphs under the Token Sliding model. In this problem, a graph is provided along…
Many existing global constraints can be encoded as a conjunction of among constraints. An among constraint holds if the number of the variables in its scope whose value belongs to a prespecified set, which we call its range, is within some…
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…
In this paper, we introduce a convergence notion for ordered selections. Our convergence notion is based on subpermutation densities and convergences of the marginal distributions. A particular case of this convergence is the well-known…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
A permutation $\pi$ contains a pattern $\sigma$ if and only if there is a subsequence in $\pi$ with its letters are in the same relative order as those in $\sigma$. Partially ordered patterns (POPs) provide a convenient way to denote…
In 1937, biologists Sturtevant and Tan posed a computational question: transform a chromosome represented by a permutation of genes, into a second permutation, using a minimum-length sequence of reversals, each inverting the order of a…
We show how an algorithm for the problem of inverting a permutation may be used to design one for the problem of unordered search (with a unique solution). Since there is a straightforward reduction in the reverse direction, the problems…
We consider the set of permutations that are sorted after two passes through a pop stack. We characterize these permutations in terms of forbidden patterns (classical and barred) and enumerate them according to the ascent statistic. Then we…
We explore various techniques to compress a permutation $\pi$ over n integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi$(i) and the application of its inverse $\pi^{-1}(i)$ in small time. Our…
Sorting networks are oblivious sorting algorithms with many practical applications and rich theoretical properties. Propositional encodings of sorting networks are a key tool for proving concrete bounds on the minimum number of comparators…
Object rearrangement is a widely-applicable and challenging task for robots. Geometric constraints must be carefully examined to avoid collisions and combinatorial issues arise as the number of objects increases. This work studies the…
We call an objective function or algorithm symmetric with respect to an input if after swapping two parts of the input in any algorithm, the solution of the algorithm and the output remain the same. More formally, for a permutation $\pi$ of…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
In a quaternion order of class number one, an element can be factored in multiple ways depending on the order of the factorization of its reduced norm. The fact that multiplication is not commutative causes an element to induce a…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
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…
A permutation $\sigma$ describing the relative orders of the first $n$ iterates of a point $x$ under a self-map $f$ of the interval $I=[0,1]$ is called an \emph{order pattern}. For fixed $f$ and $n$, measuring the points $x\in I$ (according…
The goal of constraint-based sequence mining is to find sequences of symbols that are included in a large number of input sequences and that satisfy some constraints specified by the user. Many constraints have been proposed in the…
Let $s$ be West's deterministic stack-sorting map. A well-known result (West) is that any length $n$ permutation can be sorted with $n-1$ iterations of $s.$ In 2020, Defant introduced the notion of highly-sorted permutations -- permutations…