Related papers: Near-Optimal Dynamic Time Warping on Run-Length En…
We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have…
Given a pattern of length $m$ and a text of length $n$, the goal in $k$-mismatch pattern matching is to compute, for every $m$-substring of the text, the exact Hamming distance to the pattern or report that it exceeds $k$. This can be…
We study dynamic $(1+\epsilon)$-approximation algorithms for the all-pairs shortest paths problem in unweighted undirected $n$-node $m$-edge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with…
We give a near-optimal quantum algorithm for the longest common substring (LCS) problem between two run-length encoded (RLE) strings, with the assumption that the prefix-sums of the run-lengths are given. Our algorithm costs…
Recently, Armstrong, Guzm\'an, and Sing Long (2021), presented an optimal $O(n^2)$ time algorithm for strict circular seriation (called also the recognition of strict quasi-circular Robinson spaces). In this paper, we give a very simple…
In this paper we provide a $\tilde{O}(m\sqrt{n})$ time algorithm that computes a $3$-multiplicative approximation of the girth of a $n$-node $m$-edge directed graph with non-negative edge lengths. This is the first algorithm which…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
In this paper we provide an $\tilde{O}(nd+d^{3})$ time randomized algorithm for solving linear programs with $d$ variables and $n$ constraints with high probability. To obtain this result we provide a robust, primal-dual…
We present a new space-efficient approach, (SparseDTW), to compute the Dynamic Time Warping (DTW) distance between two time series that always yields the optimal result. This is in contrast to other known approaches which typically…
Given $n$ intervals on a line $\ell$, we consider the problem of moving these intervals on $\ell$ such that no two intervals overlap and the maximum moving distance of the intervals is minimized. The difficulty for solving the problem lies…
We give a 3/2-approximation algorithm for stable matchings that runs in $O(m)$ time. The previously best known algorithm by McDermid has the same approximation ratio but runs in $O(n^{3/2}m)$ time, where $n$ denotes the number of people and…
Continuous Dynamic Time Warping (CDTW) is a robust similarity measure for polygonal curves that has recently found a variety of applications. Despite its practical use, not much is known about the algorithmic complexity of computing it in…
We present two randomised approximate counting algorithms with $\widetilde{O}(n^{2-c}/\varepsilon^2)$ running time for some constant $c>0$ and accuracy $\varepsilon$: (1) for the hard-core model with fugacity $\lambda$ on graphs with…
We present an $\tilde{O}(m^{10/7})=\tilde{O}(m^{1.43})$-time algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities. This is the first improvement over the sparse-graph case of the…
We show how to determine whether a given pattern p of length m occurs in a given text t of length n in ${\tilde O}(\sqrt{n}+\sqrt{m})$\footnote{${\tilde O}$ allows for logarithmic factors in m and $n/m$} time, with inverse polynomial…
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 $n$,…
Given a metric space $(X,d_X)$, the earth mover distance between two distributions over $X$ is defined as the minimum cost of a bipartite matching between the two distributions. The doubling dimension of a metric $(X, d_X)$ is the smallest…
The edit distance between two rooted ordered trees with $n$ nodes labeled from an alphabet~$\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling…
In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and…
Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - \epsilon)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / \epsilon) ^ {2 - o(1)}$ based on the $(\min,…