相关论文: Considering Adelman's Shortest Permutation Strings

Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…

We present two variations of Duval's algorithm for computing the Lyndon factorization of a word. The first algorithm is designed for the case of small alphabets and is able to skip a significant portion of the characters of the string, for…

A reduced word of a permutation $w$ is a minimal length expression of $w$ as a product of simple transpositions. We examine the computational complexity, formulas and (randomized) algorithms for their enumeration. In particular, we prove…

Combinatorial designs provide an interesting source of optimization problems. Among them, permutation codes are particularly interesting given their applications in powerline communications, flash memories, and block ciphers. This paper…

Given a string $w$, another string $v$ is said to be a subsequence of $w$ if $v$ can be obtained from $w$ by removing some of its letters; on the other hand, $v$ is called an absent subsequence of $w$ if $v$ is not a subsequence of $w$. The…

We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such…

In this paper, a method to generate permutations of a string under a set of constraints decided by the user is presented. The required permutations are generated without generating all the permutations.

In the Shortest-Superstring problem, we are given a set of strings S and want to find a string that contains all strings in S as substrings and has minimum length. This is a classical problem in approximation and the best known…

We provide general criteria for the existence of minimal models of streaming transducers, namely devices that read an input word and produce an output value by iteratively updating an internal memory. This abstract model subsumes classical…

We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…

Strings are a natural representation of biological data such as DNA, RNA and protein sequences. The problem of finding a string that summarizes a set of sequences has direct application in relative compression algorithms for genome and…

This paper proposes a new algorithm for generating all permutations of multisets. The method uses transpositions only and adjacent transpositions are favoured. The algorithm requires a strong homogeneous transposition condition:…

In the well-known Minimum Linear Arrangement problem (MinLA), the goal is to arrange the nodes of an undirected graph into a permutation so that the total stretch of the edges is minimized. This paper studies an online (learning) variant of…

An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…

Is it possible to find a shortest description for a binary string? The well-known answer is "no, Kolmogorov complexity is not computable." Faced with this barrier, one might instead seek a short list of candidates which includes a laconic…

We examine the open problem of finding the shortest string that contains each of the n! permutations of n symbols as contiguous substrings (i.e., the shortest superpermutation on n symbols). It has been conjectured that the shortest…

In this short paper, we present an improved algorithm for approximating the minimum cut on distributed (CONGEST) networks. Let $\lambda$ be the minimum cut. Our algorithm can compute $\lambda$ exactly in…

We introduce a novel definition of approximate palindromes in strings, and provide an algorithm to find all maximal approximate palindromes in a string with up to $k$ errors. Our definition is based on the usual edit operations of…

Interleaved learning in machine learning algorithms is a biologically inspired training method with promising results. In this short note, we illustrate the interleaving mechanism via a simple statistical and optimization framework based on…

We comment on two randomized algorithms for constructing low-rank matrix decompositions. Both algorithms employ the Subsampled Randomized Hadamard Transform [14]. The first algorithm appeared recently in [9]; here, we provide a novel…