Related papers: Two Error Bounds of Imperfect Binary Search

Assume that a target is known to be present at an unknown point among a finite set of locations in the plane. We search for it using a mobile robot that has imperfect sensing capabilities. It takes time for the robot to move between…

This report investigates three fundamental search algorithms: Linear Search, Binary Search, and Two Pointer Search. Linear Search checks each element sequentially, Binary Search divides the search space in half, and Two Pointer Search uses…

We introduce a search problem generalizing the typical setting of Binary Search on the line. Similar to the setting for Binary Search, a target is chosen adversarially on the line, and in response to a query, the algorithm learns whether…

We consider a simple optimal probabilistic problem solving strategy that searches through potential solution candidates in a specific order. We are interested in what impact has interchanging the order of two solution candidates with…

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…

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…

We make two contributions to the problem of estimating the $L_1$ calibration error of a binary classifier from a finite dataset. First, we provide an upper bound for any classifier where the calibration function has bounded variation.…

Detection of symmetry is vital to problem solving. Most of the problems of computer vision and computer graphics and machine intelligence in general, can be reduced to symmetry detection problem. Unstructured search problem can also be…

Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is…

Weighted Hamming distance, as a similarity measure between binary codes and binary queries, provides superior accuracy in search tasks than Hamming distance. However, how to efficiently and accurately find $K$ binary codes that have the…

This work generalizes the binary search problem to a $d$-dimensional domain $S_1\times\cdots\times S_d$, where $S_i=\{0, 1, \ldots,n_i-1\}$ and $d\geq 1$, in the following way. Given $(t_1,\ldots,t_d)$, the target element to be found, the…

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…

In this paper, based on results of exact learning and test theory, we study arbitrary infinite binary information systems each of which consists of an infinite set of elements and an infinite set of two-valued functions (attributes) defined…

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…

Binary codes are widely used to represent the data due to their small storage and efficient computation. However, there exists an ambiguity problem that lots of binary codes share the same Hamming distance to a query. To alleviate the…

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 explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…

Binary classification involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound).…

Our study revisits the problem of accuracy-fairness tradeoff in binary classification. We argue that comparison of non-discriminatory classifiers needs to account for different rates of positive predictions, otherwise conclusions about…

Among the various aspects of algorithmic fairness studied in recent years, the tension between satisfying both \textit{sufficiency} and \textit{separation} -- e.g. the ratios of positive or negative predictive values, and false positive or…