Related papers: Constant factor approximations to edit distance on…
In the trace reconstruction problem, the goal is to reconstruct an unknown string $x$ of length $n$ from multiple traces obtained by passing $x$ through the deletion channel. In the relaxed problem of $approximate$ trace reconstruction, the…
We design new approximation algorithms for the Multiway Cut problem, improving the previously known factor of 1.32388 [Buchbinder et al., 2013]. We proceed in three steps. First, we analyze the rounding scheme of Buchbinder et al., 2013 and…
A border of a string is a non-empty proper prefix of the string that is also a suffix. A string is unbordered if it has no border. The longest unbordered factor is a fundamental notion in stringology, closely related to string periodicity.…
We provide deterministic, polynomial-time computable voting rules that approximate Dodgson's and (the ``minimization version'' of) Young's scoring rules to within a logarithmic factor. Our approximation of Dodgson's rule is tight up to a…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
Approximate Pattern Matching is among the most fundamental string-processing tasks. Given a text $T$ of length $n$, a pattern $P$ of length $m$, and a threshold $k$, the task is to identify the fragments of $T$ that are at distance at most…
We give the first constant-factor approximation for the Directed Latency problem in quasi-polynomial time. Here, the goal is to visit all nodes in an asymmetric metric with a single vehicle starting at a depot $r$ to minimize the average…
Several measures exist for string similarity, including notable ones like the edit distance and the indel distance. The former measures the count of insertions, deletions, and substitutions required to transform one string into another,…
We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational…
Real-world data often comes in compressed form. Analyzing compressed data directly (without decompressing it) can save space and time by orders of magnitude. In this work, we focus on fundamental sequence comparison problems and try to…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
We present an efficient algorithm for finding all approximate occurrences of a given pattern $p$ of length $m$ in a text $t$ of length $n$ allowing for translocations of equal length adjacent factors and inversions of factors. The algorithm…
This paper is concerned with practical implementations of approximate string dictionaries that allow edit errors. In this problem, we have as input a dictionary $D$ of $d$ strings of total length $n$ over an alphabet of size $\sigma$. Given…
In this paper, we design new sublinear-time algorithms for solving the gap edit distance problem and for embedding edit distance to Hamming distance. For the gap edit distance problem, we give an $\tilde{O}(\frac{n}{k}+k^2)$-time greedy…
Analyzing patterns in data streams generated by network traffic, sensor networks, or satellite feeds is a challenge for systems in which the available storage is limited. In addition, real data is noisy, which makes designing data stream…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
Let $\{p_1, \ldots , p_n \} \subset {\Bbb{R}}^2$ be a separated point set, i.e., any two points have a distance at least $1$. Let $k \ge 1$ be an integer, and $1 \le t_1 < \ldots < t_k$ be real numbers. Let $\delta > 0$. Suppose for all $1…
We study the problem of edit similarity joins, where given a set of strings and a threshold value $K$, we want to output all pairs of strings whose edit distances are at most $K$. Edit similarity join is a fundamental problem in data…
Consider a metric space $(P,dist)$ with $N$ points whose doubling dimension is a constant. We present a simple, randomized, and recursive algorithm that computes, in $O(N \log N)$ expected time, the closest-pair distance in $P$. To generate…
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…