Related papers: Recovery from Non-Decomposable Distance Oracles
Dynamic Time Wrapping (DTW) is a widely used algorithm for measuring similarities between two time series. It is especially valuable in a wide variety of applications, such as clustering, anomaly detection, classification, or video…
A distance oracle is a compact representation of the shortest distance matrix of a graph. It can be queried to approximate shortest paths between any pair of vertices. Any distance oracle that returns paths of worst-case stretch (2k-1) must…
The paper considers various formalisms based on Automata, Temporal Logic and Regular Expressions for specifying queries over sequences. Unlike traditional binary semantics, the paper presents a similarity based semantics for thse…
The well-known trace reconstruction problem is the problem of inferring an unknown source string $x \in \{0,1\}^n$ from independent "traces", i.e. copies of $x$ that have been corrupted by a $\delta$-deletion channel which independently…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
This work studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and non-binary sequences from synchronization (insertion/deletion-correcting) codes.…
In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and…
Exact reconstruction of an image from measurements of its Discrete Fourier Transform (DFT) typically requires all DFT coefficients to be available. However, incorporating the prior assumption that the image contains only integer values…
The approximate period recovery problem asks to compute all $\textit{approximate word-periods}$ of a given word $S$ of length $n$: all primitive words $P$ ($|P|=p$) which have a periodic extension at edit distance smaller than $\tau_p$ from…
Wireless sensor networks are widely adopted in military, civilian and commercial applications, which fuels an exponential explosion of sensory data. However, a major challenge to deploy effective sensing systems is the presence of {\em…
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $\varphi$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential…
The Fr\'echet distance is a popular distance measure between trajectories or curves in space, or between walks in graphs. We study computing the Fr\'echet distance between walks in the $d$-dimensional grid graphs, i.e. $\mathbb{Z}^d$ where…
For pattern recognition like image recognition, it has become clear that each machine-learning dictionary data actually became data in probability space belonging to Euclidean space. However, the distances in the Euclidean space and the…
V. Levenshtein first proposed the sequence reconstruction problem in 2001. This problem studies the model where the same sequence from some set is transmitted over multiple channels, and the decoder receives the different outputs. Assume…
We consider the problem of recovering a complete (i.e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb R^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse. This…
A function $f : \mathbb{F}_2^n \to \mathbb{R}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. Motivated by applications to fast sparse Fourier transforms over $\mathbb{F}_2^n$, we study efficient algorithms for the…
Distance oracles are data structures that provide fast (possibly approximate) answers to shortest-path and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular…
Learning from data in the presence of outliers is a fundamental problem in statistics. In this work, we study robust statistics in the presence of overwhelming outliers for the fundamental problem of subspace recovery. Given a dataset where…
The Dynamic Time Warping (DTW) distance is a popular measure of similarity for a variety of sequence data. For comparing polygonal curves $\pi, \sigma$ in $\mathbb{R}^d$, it provides a robust, outlier-insensitive alternative to the…
Distance geometry explores the properties of distance spaces that can be exactly represented as the pairwise Euclidean distances between points in $\mathbb{R}^d$ ($d \geq 1$), or equivalently, distance spaces that can be isometrically…