Related papers: On multidimensional generalization of binary searc…
Similar subtrajectory search is a finer-grained operator that can better capture the similarities between one query trajectory and a portion of a data trajectory than the traditional similar trajectory search, which requires the two checked…
We consider the problem of searching a d-dimensional lattice of N sites for a single marked location. We present a Hamiltonian that solves this problem in time of order sqrt(N) for d>2 and of order sqrt(N) log(N) in the critical dimension…
Suppose we know that an object is in a sorted table and we want to determine the index of that object. To achieve this goal we could perform a binary search. However, suppose it is time-consuming to determine the relative position of that…
Consider the following generalization of the classic binary search problem: a searcher is required to find a hidden vertex $x$ in a tree $T$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$. After…
We prove that for any positive integers $n$ and $d$ there exists a collection consisting of $f=d\log n+O(1)$ subsets $A_1, A_2, \ldots, A_f$ of $[n]$ such that for any two distinct subsets $X$ and $Y$ of $[n]$ whose size is at most $d$…
This paper considers the task of performing binary search under noisy decisions, focusing on the application of target area localization. In the presence of noise, the classical partitioning approach of binary search is prone to error…
The problem of content search through comparisons has recently received considerable attention. In short, a user searching for a target object navigates through a database in the following manner: the user is asked to select the object most…
A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown…
Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial…
In this research endeavor, some Sequence Alignment Algorithms are detailed that are useful for finding or comparing 1 dimensional (1-D), 2 dimensional (2-D), 3 dimensional (3-D) sequences in or against a parent or mother database which is 1…
Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in $\mathbb{R}^{d}$ with an optimal number of samples. We generalize this problem to the case of spatial signals,…
Basically information means selection within a domain (value or definition set) of possibilities. For objectifiable, comparable and precise information the domain should be the same for all. Therefore the global (online) definition of the…
The $k$-d tree is one of the oldest and most widely used data structures for nearest neighbor search. It partitions Euclidean space into axis-aligned rectangular cells. There are two standard ways to find the nearest neighbor to a query in…
Given a set S of n \geq d points in general position in R^d, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a…
Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…
Many canonical machine learning problems boil down to a convex optimization problem with a finite sum structure. However, whereas much progress has been made in developing faster algorithms for this setting, the inherent limitations of…
This paper proposes a modification to the traditional binary search algorithm in which it checks the presence of the input element with the middle element of the given set of elements at each iteration. Modified binary search algorithm…
Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of n items and we would like to find a marked item. We consider a new variant of this problem in which…