Related papers: The n-dimensional k-vector and its application to …
A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
Range-filtering approximate nearest neighbor (RFANN) search is attracting increasing attention in academia and industry. Given a set of data objects, each being a pair of a high-dimensional vector and a numeric value, an RFANN query with a…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
Embedding models can generate high-dimensional vectors whose similarity reflects semantic affinities. Thus, accurately and timely retrieving those vectors in a large collection that are similar to a given query has become a critical…
Approximate K nearest neighbor (AKNN) search is a fundamental and challenging problem. We observe that in high-dimensional space, the time consumption of nearly all AKNN algorithms is dominated by that of the distance comparison operations…
Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…
Change-point analysis is thriving in this big data era to address problems arising in many fields where massive data sequences are collected to study complicated phenomena over time. It plays an important role in processing these data by…
We study the k nearest neighbors problem in the plane for general, convex, pairwise disjoint sites of constant description complexity such as line segments, disks, and quadrilaterals and with respect to a general family of distance…
We study the following problem: preprocess a set O of objects into a data structure that allows us to efficiently report all pairs of objects from O that intersect inside an axis-aligned query range Q. We present data structures of size…
Robots operating in households must find objects on shelves, under tables, and in cupboards. In such environments, it is crucial to search efficiently at 3D scale while coping with limited field of view and the complexity of searching for…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
With the continuous popularity of deep learning and representation learning, fast vector search becomes a vital task in various ranking/retrieval based applications, say recommendation, ads ranking and question answering. Neural network…
We show a simple generalization of the quantum walk algorithm for search in backtracking trees by Montanaro (ToC 2018) to the case where vertices can have different times of computation. If a vertex $v$ in the tree of depth $D$ is computed…
Architecture sizes for neural networks have been studied widely and several search methods have been offered to find the best architecture size in the shortest amount of time possible. In this paper, we study compact neural network…
Grover's algorithm is normally presented as a method of searching a database, however it would be more accurately described as a method of identifying elements of an interval of the integers which satisfy some logical clause - an example…
With the advancement of machine learning and deep learning, vector search becomes instrumental to many information retrieval systems, to search and find best matches to user queries based on their semantic similarities.These online services…
We propose a general framework for end-to-end learning of data structures. Our framework adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned…
Learned top-K search is a promising approach for serving vector queries with both high accuracy and performance. However, current models trained for a specific K value fail to generalize to real-world multi-K queries: they suffer from…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…