Related papers: A Faster Algorithm for Finding Closest Pairs in Ha…
We consider a similarity measure between two sets $A$ and $B$ of vectors, that balances the average and maximum cosine distance between pairs of vectors, one from set $A$ and one from set $B$. As a motivation for this measure, we present…
We introduce two novel algorithms for the problem of finding the closest pair in a cloud of $n$ points based on findings from mathematical optimal packing theory. Both algorithms are deterministic, show fast effective runtimes, and are very…
The aim of this paper is to endow the well-known family of hypercubic quantization hashing methods with theoretical guarantees. In hypercubic quantization, applying a suitable (random or learned) rotation after dimensionality reduction has…
Nearest neighbor search is a very active field in machine learning for it appears in many application cases, including classification and object retrieval. In its canonical version, the complexity of the search is linear with both the…
String matching is the problem of finding all the occurrences of a pattern in a text. We propose improved versions of the fast family of string matching algorithms based on hashing $q$-grams. The improvement consists of considering minimal…
Modern approaches for fast retrieval of similar vectors on billion-scaled datasets rely on compressed-domain approaches such as binary sketches or product quantization. These methods minimize a certain loss, typically the mean squared error…
The closest pair problem (CPP) is one of the well studied and fundamental problems in computing. Given a set of points in a metric space, the problem is to identify the pair of closest points. Another closely related problem is the fixed…
We consider the problem of computing a $(1+\epsilon)$-approximation of the Hamming distance between a pattern of length $n$ and successive substrings of a stream. We first look at the one-way randomised communication complexity of this…
Hashing methods have been widely investigated for fast approximate nearest neighbor searching in large data sets. Most existing methods use binary vectors in lower dimensional spaces to represent data points that are usually real vectors of…
This paper proposes a generic formulation that significantly expedites the training and deployment of image classification models, particularly under the scenarios of many image categories and high feature dimensions. As a defining…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
Hashing method maps similar data to binary hashcodes with smaller hamming distance, and it has received a broad attention due to its low storage cost and fast retrieval speed. However, the existing limitations make the present algorithms…
In the classical best approximation pair (BAP) problem, one is given two nonempty, closed, convex and disjoint subsets in a finite- or an infinite-dimensional Hilbert space, and the goal is to find a pair of points, each from each subset,…
We consider approximate circular pattern matching (CPM, in short) under the Hamming and edit distance, in which we are given a length-$n$ text $T$, a length-$m$ pattern $P$, and a threshold $k>0$, and we are to report all starting positions…
Computing all-pairs shortest paths is a fundamental and much-studied problem with many applications. Unfortunately, despite intense study, there are still no significantly faster algorithms for it than the $\mathcal{O}(n^3)$ time algorithm…
In the Maximum Duo-Preservation String Mapping problem we are given two strings and wish to map the letters of the former to the letters of the latter so as to maximise the number of duos. A duo is a pair of consecutive letters that is…
We generalize the monotone local search approach of Fomin, Gaspers, Lokshtanov and Saurabh [J. ACM 2019], by establishing a connection between parameterized approximation and exponential-time approximation algorithms for monotone subset…
Suppose that we have two similar files stored on different computers. We need to send the file from the first computer to the second one trying to minimize the number of bits transmitted. This article presents a survey of results known for…
This paper proposes a binarization scheme for vectors of high dimension based on the recent concept of anti-sparse coding, and shows its excellent performance for approximate nearest neighbor search. Unlike other binarization schemes, this…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…