We consider two active binary-classification problems with atypical objectives. In the first, active search, our goal is to actively uncover as many members of a given class as possible. In the second, active surveying, our goal is to actively query points to ultimately predict the proportion of a given class. Numerous real-world problems can be framed in these terms, and in either case typical...

We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: • Each comparison is erroneous with independent probability 1− p. • At each stage k comparisons can be performed in parallel and a noisy answer is returned. We present a (classical) algorithm which solves both variants optimally (with respect to p and k), up to an additive term of O(loglog ...

LetCn denote the number of nodes in a random binary search tree (of n nodes) at the maximal level. In this paper we present a direct proof of Robson’s boundedness conjecture saying that the expected values ECn remain bounded as n → ∞. We also prove that ECn is asymptotically (multiplicatively) periodic which shows that Robson’s convergence conjecture (that is, ECn is convergent) is only true if...

We present a new code (companion) that identifies bound systems of particles in O(N logN) time. Simple binaries consisting of pairs of mutually bound particles and complex hierarchies consisting of collections of mutually bound particles are identifiable with this code. In comparison, brute force binary search methods scale as O(N2) while full hierarchy searches can be as expensive as O(N3), ma...

Differential Evolution (DE) has been applied to many scientific and engineering problems for its simplicity and efficiency. However, the standard DE cannot be used in a binary search space directly. This paper proposes an adaptive binary Differential Evolution algorithm, or ABDE, that has a similar framework as the standard DE but with an improved binary mutation strategy in which the best indi...

Franzkeit, R., A binary search problem on graphs, Discrete Applied Mathematics 36 (1992) 83-86. Let G = (V, E) be a graph and e’~ E an unknown edge. I:, order to find e’ we choose a sequence of test sets WC V, where aftev every test we are told whether both vertices incident to e’ are in W, or not. For C(Gj, L,,~ Aminimum number of tests required, the inequality c(G)? rlogz 1~11 clearly holds (...

This paper describes an algorithm for Successive Approximation Register (SAR) ADCs with overlapping steps that allow comparison decision errors (due to, such as DAC incomplete settling) to be digitally corrected. We generalize this non-binary search algorithm, and clarify which decision errors it can digitally correct. This algorithm requires more SAR ADC conversion steps than a binary search a...

Deletions in binary search trees are difficult to analyse as they are not randomness preserving. We present a new kind of tree which differs slightly from the standard binary search tree. It is referred to as an ordered binary search tree as it stores a history element in its nodes, which provides information about the order in which the nodes were inserted. Using this extra information it is p...

Figure 1: a binary tree Search trees are tree-based data structures that can be used to store and search for items that satisfy a total order. There are many types of search trees designed for a wide variety of purposes. Probably, the most common use is to implement sets and tables (dictionaries, mappings). As shown on right, a binary tree is a tree in which every node in the tree has at most t...