Related papers: An $\mathcal{O}(n)$ Space Construction of Superper…
A universal cycle for permutations of length $n$ is a cyclic word or permutation, any factor of which is order-isomorphic to exactly one permutation of length $n$, and containing all permutations of length $n$ as factors. It is well known…
This paper reformulates the problem of finding a longest common increasing subsequence of the two given input sequences in a very succinct way. An extremely simple linear space algorithm based on the new formula can find a longest common…
Set intersection is a fundamental operation in information retrieval and database systems. This paper introduces linear space data structures to represent sets such that their intersection can be computed in a worst-case efficient way. In…
We present a data structure that stores a sequence $s[1..n]$ over alphabet $[1..\sigma]$ in $n\Ho(s) + o(n)(\Ho(s){+}1)$ bits, where $\Ho(s)$ is the zero-order entropy of $s$. This structure supports the queries \access, \rank\ and \select,…
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…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
In an $n \times n$ array filled with symbols, a transversal is a collection of entries with distinct rows, columns and symbols. In this note we show that if no symbol appears more than $\beta n$ times, the array contains a transversal of…
A permutation $\sigma \in S_n$ is a $k$-superpattern (or $k$-universal) if it contains each $\tau \in S_k$ as a pattern. This notion of "superpatterns" can be generalized to words on smaller alphabets, and several questions about…
A permutation array(permutation code, PA) of length $n$ and distance $d$, denoted by $(n,d)$ PA, is a set of permutations $C$ from some fixed set of $n$ elements such that the Hamming distance between distinct members…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $\tau$ times in $S$, for some integer $\tau\in[1,n]$. We…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…
A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the…
Packing density is a permutation occurrence statistic which describes the maximal number of permutations of a given type that can occur in another permutation. In this article we focus on containment of sets of permutations. Although this…
We investigate retransmission permutation arrays (RPAs) that are motivated by applications in overlapping channel transmissions. An RPA is an $n\times n$ array in which each row is a permutation of ${1, ..., n}$, and for $1\leq i\leq n$,…
We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…
The reconstruction problem for permutations on $n$ elements from their erroneous patterns which are distorted by transpositions is presented in this paper. It is shown that for any $n \geq 3$ an unknown permutation is uniquely…
Motivated by the problem of redistricting, we study area-preserving reconfigurations of connected subdivisions of a simple polygon. A connected subdivision of a polygon $\mathcal{R}$, called a district map, is a set of interior disjoint…
We define the operation of composing two hereditary classes of permutations using the standard composition of permutations as functions and we explore properties and structure of permutation classes considering this operation. We mostly…
We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial…