Related papers: Approximating the Median under the Ulam Metric
The classical rank aggregation problem seeks to combine a set X of n permutations into a single representative "consensus" permutation. In this paper, we investigate two fundamental rank aggregation tasks under the well-studied Ulam metric:…
Given a set of strings over a specified alphabet, identifying a median or consensus string that minimizes the total distance to all input strings is a fundamental data aggregation problem. When the Hamming distance is considered as the…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
We present a near-linear time algorithm that approximates the edit distance between two strings within a polylogarithmic factor; specifically, for strings of length n and every fixed epsilon>0, it can compute a (log n)^O(1/epsilon)…
The Median String Problem is W[1]-Hard under the Levenshtein distance, thus, approximation heuristics are used. Perturbation-based heuristics have been proved to be very competitive as regards the ratio approximation accuracy/convergence…
We study the classical metric $k$-median clustering problem over a set of input rankings (i.e., permutations), which has myriad applications, from social-choice theory to web search and databases. A folklore algorithm provides a…
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…
We consider an \emph{approximate} version of the trace reconstruction problem, where the goal is to recover an unknown string $s\in\{0,1\}^n$ from $m$ traces (each trace is generated independently by passing $s$ through a probabilistic…
We consider the following model for sampling pairs of strings: $s_1$ is a uniformly random bitstring of length $n$, and $s_2$ is the bitstring arrived at by applying substitutions, insertions, and deletions to each bit of $s_1$ with some…
Edit distance is a fundamental measure of distance between strings and has been widely studied in computer science. While the problem of estimating edit distance has been studied extensively, the equally important question of actually…
Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However,…
The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamic programming solution for this problem computes the edit-distance between…
We consider the classic 1-center problem: Given a set $P$ of $n$ points in a metric space find the point in $P$ that minimizes the maximum distance to the other points of $P$. We study the complexity of this problem in $d$-dimensional…
We give a polynomial-time approximation algorithm for the (not necessarily metric) $k$-Median problem. The algorithm is an $\alpha$-size-approximation algorithm for $\alpha < 1 + 2 \ln(n/k)$. That is, it guarantees a solution having size at…
Many consensus string problems are based on Hamming distance. We replace Hamming distance by the more flexible (e.g., easily coping with different input string lengths) dynamic time warping distance, best known from applications in time…
We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…
We study approximation algorithms for the following three string measures that are widely used in practice: edit distance (ED), longest common subsequence (LCS), and longest increasing sequence (LIS). All three problems can be solved…
Rank aggregation seeks a representative permutation for a collection of rankings and plays a central role in areas such as social choice, information retrieval, and computational biology. Two fundamental aggregation tasks are the center and…
The problem of finding a center string that is `close' to every given string arises and has many applications in computational biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring…
The edit distance is a fundamental measure of sequence similarity, defined as the minimum number of character insertions, deletions, and substitutions needed to transform one string into the other. Given two strings of length at most $n$,…