Related papers: Near-Optimal Compressive Binary Search

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…

This work considers the problem of the noisy binary search in a sorted array. The noise is modeled by a parameter $p$ that dictates that a comparison can be incorrect with probability $p$, independently of other queries. We state two types…

The problem of monotone submodular maximization has been studied extensively due to its wide range of applications. However, there are cases where one can only access the objective function in a distorted or noisy form because of the…

In this paper we consider the problem of locating a nonzero entry in a high-dimensional vector from possibly adaptive linear measurements. We consider a recursive bisection method which we dub the compressive binary search and show that it…

Binary search finds a given element in a sorted array with an optimal number of $\log n$ queries. However, binary search fails even when the array is only slightly disordered or access to its elements is subject to errors. We study the…

We find a searching method on ordered lists that surprisingly outperforms binary searching with respect to average query complexity while retaining minmax optimality. The method is shown to require $O(\log_2\log_2 n)$ queries on average…

This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible…

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…

We revisit the classical algorithms for searching over sorted sets to introduce an algorithm refinement, called Adaptive Search, that combines the good features of Interpolation search and those of Binary search. W.r.t. Interpolation…

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…

In this paper, we propose a stand-alone mobile visual search system based on binary features and the bag-of-visual words framework. The contribution of this study is three-fold: (1) We propose an adaptive substring extraction method that…

This paper describes an efficient reduction of the learning problem of ranking to binary classification. The reduction guarantees an average pairwise misranking regret of at most that of the binary classifier regret, improving a recent…

Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This has been proved to be the best possible algorithm for the exhuastive search problem in the sense the number of queries it requires…

Sorting is a fundamental problem in computer science. In the classical setting, it is well-known that $(1\pm o(1)) n\log_2 n$ comparisons are both necessary and sufficient to sort a list of $n$ elements. In this paper, we study the Noisy…

The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and has numerous practical applications. One of the defining features of group testing is…

Compression has emerged as one of the essential deep learning research topics, especially for the edge devices that have limited computation power and storage capacity. Among the main compression techniques, low-rank compression via matrix…

In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…

Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…