Related papers: Average-case analysis of perfect sorting by revers…
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…
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…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
In-place associative integer sorting technique was developed, improved and specialized for distinct integers. The technique is suitable for integer sorting. Hence, given a list S of n integers S[0...n-1], the technique sorts the integers in…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
We show that the theory of sorting by reversals fits into the well-established theory of circuit partitions of 4-regular multigraphs (which also involves the combinatorial structures of circle graphs and delta-matroids). In this way, we…
Common intervals have been defined as a modelisation of gene clusters in genomes represented either as permutations or as sequences. Whereas optimal algorithms for finding common intervals in permutations exist even for an arbitrary number…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
Permutation sorting, one of the fundamental steps in pre-processing data for the efficient application of other algorithms, has a long history in mathematical research literature and has numerous applications. Two special-purpose sorting…
Backtrack search is a fundamental technique for computing with finite permutation groups, which has been formulated in terms of points, ordered partitions, and graphs. We provide a framework for discussing the most common forms of backtrack…
There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and…
We consider the well-studied pattern counting problem: given a permutation $\pi \in \mathbb{S}_n$ and an integer $k > 1$, count the number of order-isomorphic occurrences of every pattern $\tau \in \mathbb{S}_k$ in $\pi$. Our first result…
We consider the question of computing the distribution of a permutation statistics over restricted permutations via enumeration schemes. The restricted permutations are those avoiding sets of vincular patterns (which include both classical…
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…
Considering a pair of genomes, the goal of rearrangement distance problems is to estimate how distant these genomes are from each other based on genome rearrangements. Seminal works in genome rearrangements assumed that both genomes being…
In this paper we present a random shuffling scheme to apply with adaptive sorting algorithms. Adaptive sorting algorithms utilize the presortedness present in a given sequence. We have probabilistically increased the amount of presortedness…
Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in…
We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…
Recursive queries have been traditionally studied in the framework of datalog, a language that restricts recursion to monotone queries over sets, which is guaranteed to converge in polynomial time in the size of the input. But modern big…