Related papers: A Faster Algorithm for Finding Closest Pairs in Ha…
All-pairs set similarity is a widely used data mining task, even for large and high-dimensional datasets. Traditionally, similarity search has focused on discovering very similar pairs, for which a variety of efficient algorithms are known.…
We propose a novel approach to charged particle tracking at high intensity particle colliders based on Approximate Nearest Neighbors search. With hundreds of thousands of measurements per collision to be reconstructed e.g. at the High…
The extension of persistent homology to multi-parameter setups is an algorithmic challenge. Since most computation tasks scale badly with the size of the input complex, an important pre-processing step consists of simplifying the input…
Similarity search is essential to many important applications and often involves searching at scale on high-dimensional data based on their similarity to a query. In biometric applications, recent vulnerability studies have shown that…
An attractive approach for fast search in image databases is binary hashing, where each high-dimensional, real-valued image is mapped onto a low-dimensional, binary vector and the search is done in this binary space. Finding the optimal…
A family of comparison-based exact pattern matching algorithms is described. They utilize multi-dimensional arrays in order to process more than one adjacent text window in each iteration of the search cycle. This approach leads to a lower…
The algorithmic tasks of computing the Hamming distance between a given pattern of length $m$ and each location in a text of length $n$ is one of the most fundamental algorithmic tasks in string algorithms. Unfortunately, there is evidence…
We show how to compute any symmetric Boolean function on $n$ variables over any field (as well as the integers) with a probabilistic polynomial of degree $O(\sqrt{n \log(1/\epsilon)})$ and error at most $\epsilon$. The degree dependence on…
We consider the problem of querying a string (or, a database) of length $N$ bits to determine all the locations where a substring (query) of length $M$ appears either exactly or is within a Hamming distance of $K$ from the query. We assume…
The indexing algorithms for the high-dimensional nearest neighbor search (NNS) with the best worst-case guarantees are based on the randomized Locality Sensitive Hashing (LSH), and its derivatives. In practice, many heuristic approaches…
Product measures of dimension $n$ are known to be concentrated in Hamming distance: for any set $S$ in the product space of probability $\epsilon$, a random point in the space, with probability $1-\delta$, has a neighbor in $S$ that is…
A common form of MapReduce application involves discovering relationships between certain pairs of inputs. Similarity joins serve as a good example of this type of problem, which we call a "some-pairs" problem. In the framework of Afrati et…
We address the problem of converting large-scale high-dimensional image data into binary codes so that approximate nearest-neighbor search over them can be efficiently performed. Different from most of the existing unsupervised approaches…
We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean…
Minwise hashing is the standard technique in the context of search and databases for efficiently estimating set (e.g., high-dimensional 0/1 vector) similarities. Recently, b-bit minwise hashing was proposed which significantly improves upon…
One of the approaches for the nearest neighbor search problem is to build a network which nodes correspond to the given set of indexed objects. In this case the search of the closest object can be thought as a search of a node in a network.…
We study the design of efficient approximation algorithms for the $\ell$-center clustering and minimum-diameter $\ell$-clustering problems in high dimensional Euclidean and Hamming spaces. Our main tool is randomized dimension reduction.…
The min-distance between two nodes $u, v$ is defined as the minimum of the distance from $v$ to $u$ or from $u$ to $v$, and is a natural distance metric in DAGs. As with the standard distance problems, the Strong Exponential Time Hypothesis…
Hashing method maps similar high-dimensional data to binary hashcodes with smaller hamming distance, and it has received broad attention due to its low storage cost and fast retrieval speed. Pairwise similarity is easily obtained and widely…
We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for…